Question 1: Palette 1/257

Errorless NEET 2024 MCQ

A particle moving with uniform speed in a circular path maintains

A

Constant velocity

B

Constant acceleration

C

Constant velocity but varying acceleration

D

Varying velocity and varying acceleration

Question 2: Palette 2/257

Errorless NEET 2024 MCQ

A bob is whirled in a horizontal plane by means of a string with an initial speed of $\omega$ rpm. The tension in the string is T. If speed becomes $2\omega$ while keeping the same radius, the tension in the string becomes

A

$T$

B

$4T$

C

$\frac{T}{4}$

D

$\sqrt{2} T$

Question 3: Palette 3/257

Errorless JEE (Main) 2023 MCQ

The maximum vertical height to which a man can throw a ball is $136m$ . The maximum horizontal distance upto which he can throw the same ball is

A

$192m$

B

$136m$

C

$272m$

D

$68m$

Question 4: Palette 4/257

Errorless JEE (Main) 2023 MCQ

A stone is projected at angle $30^{\circ}$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be

A

1:2

B

1:4

C

4:1

D

4:3

Question 5: Palette 5/257

Errorless JEE (Main) 2023 MCQ

The initial speed of a projectile fired form ground is u. At the highest point during its motion, the speed of projectile $\frac{\sqrt{3}}{2}u$ . The time of flight of the projectile is

A

$\frac{u}{2g}$

B

$\frac{u}{g}$

C

$\frac{2u}{g}$

D

$\frac{\sqrt{3}u}{g}$

Question 6: Palette 6/257

Errorless JEE (Main) 2023 MCQ

A body is moving with constant speed, in a circle of radius 10m. The body completes one revolution in 4s. At the end of 3rd second, the displacement of body (in m) from its starting point is

A

30

B

$15\pi$

C

$5\pi$

D

$10\sqrt{2}$

Question 7: Palette 7/257

Errorless JEE (Main) 2023 MCQ

For a body projected at an angle with the horizontal from the ground, choose the correct statement

A

Gravitational potential energy is maximum at the highest point.

B

The horizontal component of velocity is zero at highest point

C

The vertical component of momentum is maximum at the highest point

D

The kinetic energy (K.E.) is zero at the highest point of projectile motion

Question 8: Palette 8/257

Errorless JEE (Main) 2023 MCQ

A car is moving with a constant speed of 20m/s in a circular horizontal track of radius 40m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be (Take g = 10m/s $^{2}$ )

A

$\frac{\pi}{6}$

B

$\frac{\pi}{2}$

C

$\frac{\pi}{4}$

D

$\frac{\pi}{3}$

Question 9: Palette 9/257

Errorless JEE (Main) 2022 MCQ

A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is

A

The same throughout the motion

B

Minimum at the highest position of the circular path

C

Minimum at the lowest position of the circular path

D

Minimum when the rope is in the horizontal position

Question 10: Palette 10/257

Errorless JEE (Main) 2022 MCQ

A person can throw a ball up to a maximum range of 100 m. How high above the ground he can throw the same ball

A

25 m

B

50 m

C

100 m

D

200 m

Question 11: Palette 11/257

Errorless JEE (Main) 2022 MCQ

A person moved from $A$ to $B$ on a circular path as shown in figure. If the distance travelled by him is $60~m$ , then the magnitude of displacement would be (Given $\cos 135^{\circ} = -0.7$ )

A

42 m

B

47m

C

19 m

D

40m

Question 12: Palette 12/257

Errorless JEE (Main) 2022 MCQ

A ball is projected with kinetic energy $E$ , at an angle of $60^{\circ}$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become

A

Zero

B

$\frac{E}{2}$

C

$\frac{E}{4}$

D

$E$

Question 13: Palette 13/257

Errorless JEE (Main) 2022 MCQ

A ball is projected from the ground with a speed $15 \, ms^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then 'tan $\theta'$ will be equal to

A

$\frac{1}{4}$

B

$\frac{1}{2}$

C

2

D

4

Question 14: Palette 14/257

Errorless JEE (Main) 2022 MCQ

Two projectiles are thrown with same initial velocity making an angle of $45^{\circ}$ and $30^{\circ}$ with the horizontal respectively. The ratio of their respective ranges will be

A

$1 : \sqrt{2}$

B

$\sqrt{2} : 1$

C

$2 : \sqrt{3}$

D

$\sqrt{3} : 2$

Question 15: Palette 15/257

Errorless JEE (Main) 2022 MCQ

Two projectiles thrown at $30^{\circ}$ and $45^{\circ}$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

A

$1:\sqrt{2}$

B

2:1

C

$\sqrt{2}:1$

D

1:2

Question 16: Palette 16/257

Errorless JEE (Main) 2022 MCQ

A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $\sqrt{x(u^{2}-gL)}$ . The value of x is

A

3

B

2

C

1

D

5

Question 17: Palette 17/257

Errorless JEE (Main) 2022 MCQ

For a particle in uniform circular motion, the acceleration $\vec{a}$ at any point $P(R,\theta)$ on the circular path of radius R is (when $\theta$ is measured from the positive x-axis and v is uniform speed)

A

$-\frac{v^{2}}{R}\sin\theta\hat{i}+\frac{v^{2}}{R}\cos\theta\hat{j}$

B

$-\frac{v^{2}}{R}\cos\theta\hat{i}+\frac{v^{2}}{R}\sin\theta\hat{j}$

C

$-\frac{v^{2}}{R}\cos\theta\hat{i}-\frac{v^{2}}{R}\sin\theta\hat{j}$

D

$-\frac{v^{2}}{R}\hat{i}+\frac{v^{2}}{R}\hat{j}$

Question 18: Palette 18/257

Errorless NEET 2022 MCQ

A ball is projected with a velocity, $10 \, ms^{-1}$ , at an angle of $60^\circ$ with the vertical direction. Its speed at the highest point of its trajectory will be

A

$5 \, ms^{-1}$

B

$10 \, ms^{-1}$

C

Zero

D

$5\sqrt{3} \, ms^{-1}$

Question 19: Palette 19/257

Errorless JEE (Main) 2021 MCQ

An electron with kinetic energy $K_{1}$ enters between parallel plates of a capacitor at an angle ' $\alpha'$ with the plates. It leaves the plates at angle ' $\beta'$ with kinetic energy $K_{2}$ . Then the ratio of kinetic energies $K_{1}:K_{2}$ will be

A

$\frac{\sin^{2}\beta}{\cos^{2}\alpha}$

B

$\frac{\cos^{2}\beta}{\cos^{2}\alpha}$

C

$\frac{\cos\beta}{\cos\alpha}$

D

$\frac{\cos\beta}{\sin\alpha}$

Question 20: Palette 20/257

Errorless JEE (Main) 2021 MCQ

The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta x^{2}$ , where $\alpha$ and $\beta$ are constants and x and y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained H are respectively given by

A

$\tan^{-1}\alpha,\frac{\alpha^{2}}{4\beta}$

B

$\tan^{-1}\beta,\frac{\alpha^{2}}{2\beta}$

C

$\tan^{-1}\beta,\frac{4\alpha^{2}}{\beta}$

D

$\tan^{-1}\left(\frac{\beta}{\alpha}\right),\frac{\alpha^{2}}{\beta}$

Question 21: Palette 21/257

Errorless JEE (Main) 2021 MCQ

Statement-I : A cyclist is moving on an unbanked road with a speed of $7kmh^{-1}$ and takes a sharp circular turn along a path of radius of 2m without reducing the speed. The static friction coefficient is 0.2. The cyclist will not slip and pass the curve ( $g = 9.8m/s^{2}$ ). Statement-II : If the road is banked at an angle of $45^{\circ}$ , cyclist can cross the curve of 2m radius with the speed of $18.5 kmh^{-1}$ without slipping. In the light of the above statements, choose the correct answer from the option given below

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 22: Palette 22/257

Errorless JEE (Main) 2021 MCQ

A modern grand-prix racing car of mass m is travelling on a flat track in a circular arc of radius R with a speed v. If the coefficient of static friction between the tyres and the track is $\mu_{s}$ , then the magnitude of negative lift $F_{L}$ acting downwards on the car is (Assume forces on the four tyres are identical and g = acceleration due to gravity)

A

$m\left(\frac{v^{2}}{\mu_{s}R}+g\right)$

B

$m\left(\frac{v^{2}}{\mu_{s}R}-g\right)$

C

$m\left(g-\frac{v^{2}}{\mu_{s}R}\right)$

D

$-m\left(g+\frac{v^{2}}{\mu_{s}R}\right)$

Question 23: Palette 23/257

Errorless JEE (Main) 2021 MCQ

A particle of mass m moves in a circular orbit under the central potential field, $U(r) = \frac{-C}{r}$ , where C is a positive constant. The correct radius–velocity graph of the particle's motion is

A

B

C

D

Question 24: Palette 24/257

Errorless JEE (Main) 2021 MCQ

A butterfly is flying with a velocity $4\sqrt{2}$ m/s in North-East direction. Wind is slowly blowing at 1m/s from North to South. The resultant displacement of the butterfly in 3 seconds is

A

3 m

B

20 m

C

$12\sqrt{2}$ m

D

15 m

Question 25: Palette 25/257

Errorless JEE (Main) 2021 MCQ

The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are $R_{1}, R_{2}$ and $H_{1}, H_{2}$ respectively. Choose the correct option

A

$R_{1} > R_{2}$ and $H_{1} = H_{2}$

B

$R_{1} = R_{2}$ and $H_{1} < H_{2}$

C

$R_{1} < R_{2}$ and $H_{1} < H_{2}$

D

$R_{1} = R_{2}$ and $H_{1} = H_{2}$

Question 26: Palette 26/257

Errorless JEE (Main) 2021 MCQ

A player kicks a football with an initial speed of $25ms^{-1}$ at an angle of $45^{\circ}$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion (Take $g = 10 ms^{-2}$ )

A

$h_{max} = 15.625m, T = 1.77s$

B

$h_{max} = 3.54m, T = 0.125s$

C

$h_{max} = 10m, T = 2.5s$

D

$h_{max} = 15.625m, T = 3.54s$

Question 27: Palette 27/257

Errorless JEE (Main) 2021 MCQ

Particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that $r=\frac{L}{\sqrt{2}}$ . The speed of particle will be

A

$\sqrt{\frac{rg}{2}}$

B

$2\sqrt{rg}$

C

$\sqrt{2rg}$

D

$\sqrt{rg}$

Question 28: Palette 28/257

Errorless NEET 2021 MCQ

A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle ' $\theta'$ to the horizontal, the maximum height attained by it equals 4R. The angle of projection $\theta$ , is then given by

A

$\theta = \cos^{-1}\left(\frac{\pi^2R}{gT^2}\right)^{1/2}$

B

$\theta = \sin^{-1}\left(\frac{\pi^2R}{gT^2}\right)^{1/2}$

C

$\theta = \sin^{-1}\left(\frac{2gT^2}{\pi^2R}\right)^{1/2}$

D

$\theta = \cos^{-1}\left(\frac{gT^2}{\pi^2R}\right)^{1/2}$

Question 29: Palette 29/257

Errorless NEET 2021 MCQ

A car starts from rest and accelerates at $5m/s^{2}$ . At t=4s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t=6s (Take $g=10m/s^{2}$ )

A

20 m/s, 0

B

$20\sqrt{2}m/s,0$

C

$20\sqrt{2}m/s,10m/s^{2}$

D

$20m/s,5m/s^{2}$

Question 30: Palette 30/257

Errorless JEE (Main) 2020 MCQ

A particle starts from the origin at t=0 with an initial velocity of $3.0\hat{i}$ m/s and moves in the x-y plane with a constant acceleration $(6.0\hat{i}+4.0\hat{j})m/s^{2}$ . The x-coordinate of the particle at the instant when its y-co-ordinate is 32 m is D meters. The value of D is

A

50

B

32

C

60

D

40

Question 31: Palette 31/257

Errorless JEE (Main) 2020 MCQ

A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height $\frac{h}{2}$ . The velocity versus height of the ball during its motion may be represented graphically by (graph are drawn schematically and on not to scale)

A

B

C

D

Question 32: Palette 32/257

Errorless JEE (Main) 2020 MCQ

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force $mkv^{2}$ where v is it speed. The maximum height attained by the ball is

A

$\frac{1}{2k}\tan^{-1}\frac{ku^{2}}{g}$

B

$\frac{1}{k}\ln\left(1+\frac{ku^{2}}{2g}\right)$

C

$\frac{1}{k}\tan^{-1}\frac{ku^{2}}{2g}$

D

$\frac{1}{2k}\ln\left(1+\frac{ku^{2}}{g}\right)$

Question 33: Palette 33/257

Errorless JEE (Main) 2020 MCQ

A clock has a continuously moving second's hand of $0.1m$ length. The average acceleration of the tip of the hand (in units of $ms^{-2}$ ) is of the order of

A

$10^{-3}$

B

$10^{-2}$

C

$10^{-4}$

D

$10^{-1}$

Question 34: Palette 34/257

Errorless JEE (Main) 2020 MCQ

A particle moving in the xy plane experiences a velocity dependent force $\vec{F} = k(v_y\hat{i} + v_x\hat{j})$ , where $v_x$ and $v_y$ are the $x$ and $y$ components of its velocity $\vec{v}$ . If $\vec{a}$ is the acceleration of the particle, then which of the following statements is true for the particle

A

Quantity $\vec{v}.\vec{a}$ is constant in time

B

Kinetic energy of particle is constant in time

C

Quantity $\vec{v} \times \vec{a}$ is constant in time

D

$\vec{F}$ arises due to a magnetic field

Question 35: Palette 35/257

Errorless JEE (Main) 2019 MCQ

The position co-ordinates of a particle moving in a 3-D coordinate system is given by $x = a \cos \omega t$ $y = a \sin \omega t$ and $z = a \omega t$ The speed of the particle is

A

$a\omega$

B

$\sqrt{3}a\omega$

C

$\sqrt{2}a\omega$

D

$2a\omega$

Question 36: Palette 36/257

Errorless JEE (Main) 2019 MCQ

Two guns A and B can fire bullets at speeds 1km/s and 2km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is

A

1:2

B

1:4

C

1:8

D

1:16

Question 37: Palette 37/257

Errorless JEE (Main) 2019 MCQ

A body is projected at t=0 with a velocity $10ms^{-1}$ at an angle of $60^{\circ}$ with the horizontal. The radius of curvature of its trajectory at t=1s is R. Neglecting air resistance and taking acceleration due to gravity $g=10ms^{-2}$ , the value of R is

A

2.5 m

B

10.3 m

C

2.8 m

D

5.1 m

Question 38: Palette 38/257

Errorless JEE (Main) 2019 MCQ

A particle is moving along a circular path with a constant speed of $10ms^{-1}$ . What is the magnitude of the change is velocity of the particle, when it moves through an angle of $60^{\circ}$ around the centre of the circle

A

Zero

B

10m/s

C

$10\sqrt{3}m/s$

D

$10\sqrt{2}m/s$

Question 39: Palette 39/257

Errorless JEE (Main) 2019 MCQ

A passenger train of length 60m travels at a speed of 80 km/hr. Another freight train of length 120m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite directions is

A

$\frac{5}{2}$

B

$\frac{25}{11}$

C

$\frac{3}{2}$

D

$\frac{11}{5}$

Question 40: Palette 40/257

Errorless JEE (Main) 2019 MCQ

A plane is inclined at an angle $\alpha = 30^{\circ}$ with a respect to the horizontal. A particle is projected with a speed $u = 2ms^{-1}$ from the base of the plane, making an angle $\theta = 15^{\circ}$ with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to (Take $g = 10ms^{-2}$ )

A

14 cm

B

20 cm

C

18 cm

D

26 cm

Question 41: Palette 41/257

Errorless JEE (Main) 2019 MCQ

The trajectory of a projectile near the surface of the earth is given as $y = 2x - 9x^2$ . If it were launched at an angle $\theta_0$ with speed $v_0$ then ( $g = 10ms^{-2}$ )

A

$\theta_0 = \cos^{-1}\left(\frac{1}{\sqrt{5}}\right)$ and $v_0 = \frac{5}{3}ms^{-1}$

B

$\theta_0 = \sin^{-1}\left(\frac{1}{\sqrt{5}}\right)$ and $v_0 = \frac{5}{3}ms^{-1}$

C

$\theta_0 = \sin^{-1}\left(\frac{2}{\sqrt{5}}\right)$ and $v_0 = \frac{3}{5}ms^{-1}$

D

$\theta_0 = \cos^{-1}\left(\frac{2}{\sqrt{5}}\right)$ and $v_0 = \frac{3}{5}ms^{-1}$

Question 42: Palette 42/257

Errorless JEE (Main) 2019 MCQ

A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is

A

$R / g$

B

$R / 4g$

C

$2R / g$

D

$R / 2g$

Question 43: Palette 43/257

Errorless JEE (Main) 2019 MCQ

A smooth wire of length $2\pi r$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $\omega$ about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of $\omega^{2}$ is equal to

A

$(g\sqrt{3}) / r$

B

$\frac{\sqrt{3}g}{2r}$

C

$2g / r$

D

$2g / (r\sqrt{3})$

Question 44: Palette 44/257

Errorless JEE (Main) 2019 MCQ

Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$ , but different maximum heights, $h_1$ and $h_2$ . Which of the following is correct

A

$R^2 = 2h_1h_2$

B

$R^2 = 16h_1h_2$

C

$R^2 = 4h_1h_2$

D

$R^2 = h_1h_2$

Question 45: Palette 45/257

Errorless NEET 2019 MCQ

A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when

A

The mass is at the highest point

B

The wire is horizontal

C

The mass is at the lowest point

D

Inclined at an angle $60^{\circ}$ from vertical

Question 46: Palette 46/257

Errorless NEET 2019 MCQ

Two particles A and B are moving in uniform circular motion in concentric circles of radius $r_{A}$ and $r_{B}$ with speed $v_{A}$ and $v_{B}$ respectively. The time period of rotation is the same. The ratio of angular speed of A to that of B will be

A

$r_{A}:r_{B}$

B

$v_{A}:v_{B}$

C

$r_{B}:r_{A}$

D

1:1

Question 47: Palette 47/257

Errorless NEET 2019 MCQ

When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ}$ with horizontal, it can travel a distance $x_{1}$ along the plane. But when the inclination is decreased to $30^{\circ}$ and the same object the shot with the same velocity, it can travel $x_{2}$ distance. Then $x_{1}: x_{2}$ will be

A

$1: \sqrt{2}$

B

$\sqrt{2}: 1$

C

$1: \sqrt{3}$

D

$1: 2\sqrt{3}$

Question 48: Palette 48/257

Errorless NEET 2017 MCQ

The x and y coordinates of the particle at any time are $x = 5t - 2t^{2}$ and y = 410t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2s is

A

0

B

$5 \, m/s^{2}$

C

$-4 \, m/s^{2}$

D

$-8 \, m/s^{2}$

Question 49: Palette 49/257

Errorless JEE (Main) 2016 MSQ

A particle of mass $m$ is moving along the side of square of side 'a' with a uniform speed $v$ in the $x - y$ plane as shown in the figure Which of the following statements is false for the angular momentum $\vec{L}$ about the origin

A

$\vec{L} = mv\left[\frac{R}{\sqrt{2}} - a\right]\hat{k}$ when the particle is moving from $C$ to $D$

B

$\vec{L}=mv\left[\frac{R}{\sqrt{2}}+a\right]\hat{k}$ when
the particle is moving from B to C

C

$\vec{L} = \frac{mv}{\sqrt{2}} R\hat{k}$ when the particle is moving from $D$ to $A$

D

$\vec{L} = -\frac{mv}{\sqrt{2}} R\hat{k}$ when the particle is moving from $A$ to $B$

Question 50: Palette 50/257

Errorless NEET (Phase-I) 2016 MCQ

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop

A

$\sqrt{gR}$

B

$\sqrt{2gR}$

C

$\sqrt{3gR}$

D

$\sqrt{5gR}$

Question 51: Palette 51/257

Errorless NEET (Phase-II) 2016 MCQ

In the given figure, $a=15m/s^{2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R=2.5 m at a given instant of time. The speed of the particle is

A

6.2 m/s

B

4.5 /s

C

5.0 m/s

D

5.7 m/s

Question 52: Palette 52/257

Errorless NEET (Phase-I) 2016 MCQ

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8 \times 10^{-4} J$ by the end of the second revolution after the beginning of the motion

A

$0.1 m/s^{2}$

B

$0.15 m/s^{2}$

C

$0.18 m/s^{2}$

D

$0.2 m/s^{2}$

Question 53: Palette 53/257

Errorless NEET (Phase-I) 2016 MCQ

A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plans and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of $2.0 \, rad \, s^{-2}$ . Its net acceleration in $ms^{-2}$ at the end of 2.0 s is approximately

A

8.0

B

7.0

C

6.0

D

3.0

Question 54: Palette 54/257

Errorless AIPMT 2015 MCQ

Two stones of masses m and 2m are whirled in horizontal circles the heavier one in radius $\frac{r}{2}$ and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is

A

3

B

4

C

1

D

2

Question 55: Palette 55/257

Errorless AIPMT 2015 MCQ

The position vector of a particle $\vec{R}$ as a function of time is given by $\vec{R} = 4\sin (2\pi t)\hat{i} +4\cos (2\pi t)\hat{j}$ where R is in meters, $t$ is seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along x- and y-directions, respectively. Which one of the following statements is wrong for the motion of particle

A

Magnitude of acceleration vector is $\frac{v^2}{R}$ , where v is the velocity of particle

B

Magnitude of the velocity of particle is $8\mathrm{m / s}$

C

Path of the particle is a circle of radius $4\mathrm{m}$

D

Acceleration vector is along - $\vec{R}$

Question 56: Palette 56/257

Errorless MH CET 2015 MCQ

The difference between angular speed of minute hand and second hand of a clock is

A

$\frac{59\pi}{900}rad/s$

B

$\frac{59\pi}{1800}rad/s$

C

$\frac{59\pi}{2400}rad/s$

D

$\frac{59\pi}{3600}rad/s$

Question 57: Palette 57/257

Errorless WB-JEE 2015 MCQ

A simple pendulum of length L swings in a vertical plane. The tension of the string when it makes an angle $\theta$ with the vertical and the bob of mass m moves with a speed v is (g is the gravitational acceleration)

A

$mv^{2}/L$

B

$mg\cos\theta + mv^{2}/L$

C

$mg\cos\theta - mv^{2}/L$

D

$mg\cos\theta$

Question 58: Palette 58/257

Errorless KCET 2015 MCQ

A particle is projected with a velocity v so that its horizontal range is twice the greatest height attained. The horizontal range is

A

$\frac{2v^{2}}{3g}$

B

$\frac{v^{2}}{2g}$

C

$\frac{v^{2}}{g}$

D

$\frac{4v^{2}}{5g}$

Question 59: Palette 59/257

Errorless KCET 2015 MCQ

The ratio of angular speed of a second-hand to the hour-hand of a watch is

A

60:1

B

72:1

C

720:1

D

3600:1

Question 60: Palette 60/257

Errorless JEE (Main) 2015 MCQ

Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first (Assume stones do not rebound after hitting the ground and neglect air resistance, take $g=10m/s^{2}$ ). (The figures are schematic and not drawn to scale)

A

B

C

D

Question 61: Palette 61/257

Errorless JEE (Main) 2013 MCQ

A projectile is given an initial velocity of $(\hat{i} + 2\hat{j})$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g = 10m/s^{2}$ , the equation of its trajectory is

A

$y = x - 5x^{2}$

B

$y = 2x - 5x^{2}$

C

$4y = 2x - 5x^{2}$

D

$4y = 2x - 25x^{2}$

Question 62: Palette 62/257

Errorless WB-JEE 2013 MCQ

A body is projected from the ground with a velocity $\vec{v} = (3\hat{i} + 10\hat{j})ms^{-1}$ . The maximum height attained and the range of the body respectively are (given $g = 10ms^{-2}$ )

A

$5m$ and $6m$

B

$3m$ and $10m$

C

$6m$ and $5m$

D

$3m$ and $5m$

Question 63: Palette 63/257

Errorless NEET 2013 MCQ

The velocity of a projectile at the initial point A is $(2\hat{i} + 3\hat{j})m/s$ . It's velocity (in m/s) at point B is

A

$2\hat{i} + 3\hat{j}$

B

$-2\hat{i} - 3\hat{j}$

C

$-2\hat{i} + 3\hat{j}$

D

$2\hat{i} - 3\hat{j}$

Question 64: Palette 64/257

Errorless NEET (Karnataka) 2013 MCQ

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track is

A

Zero

B

30°

C

45°

D

60°

Question 65: Palette 65/257

Errorless CBSE PMT (Pre.) 2012 MCQ

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is $45^{\circ}$ , the speed of the car is

A

$20 ms^{-1}$

B

$30 ms^{-1}$

C

$5 ms^{-1}$

D

$10 ms^{-1}$

Question 66: Palette 66/257

Errorless Odisha JEE 2012 MCQ

A body moves in a circle covers equal distance in equal intervals of time. Which of the following remains constant

A

Velocity

B

Acceleration

C

Speed

D

Displacement

Question 67: Palette 67/257

Errorless Kerala PMT 2012 MCQ

A particle of mass m describes uniform circular motion in a horizontal plane. The quantity that is conserved is

A

Linear velocity

B

Linear momentum

C

Angular momentum

D

Linear acceleration

E

Angular displacement

Question 68: Palette 68/257

Errorless AMU (Med.) 2012 MCQ

A particle moves in a circular orbit of radius $r$ under a central attractive force $F = -\frac{k}{r}, k$ is constant. The time period of its motion shall be proportional to

A

$r^{1/2}$

B

$r$

C

$r^{3/2}$

D

$r^{2/3}$

Question 69: Palette 69/257

Errorless J & K CET 2012 MCQ

A brick of mass m, tied to a rope, is being whirled in a vertical circle, with a uniform speed. The tension in the rope is

A

The same throughout

B

Largest when the brick is at the highest point of the circular path and smallest when it is at the lowest point

C

Largest when the rope is horizontal and smallest when it is vertical

D

Largest when the brick is at the lowest point and smallest when it is at the highest point

Question 70: Palette 70/257

Errorless AIEEE 2012 MCQ

Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is

A

$m_{1}r_{1}:m_{2}r_{2}$

B

$m_{1}:m_{2}$

C

$r_{1}:r_{2}$

D

1:1

Question 71: Palette 71/257

Errorless AMU (Engg.) 2012 MCQ

What is approximately the centripetal acceleration (in units of acceleration due to gravity on earth, $g = 10 \, m/s^{2}$ ) of an air-craft flying at a speed of 400 m/s through a circular arc of radius 0.6 km

A

26.7

B

16.9

C

13.5

D

30.2

Question 72: Palette 72/257

Errorless Kerala PMT 2012 MCQ

If the velocity (in $ms^{-1}$ ) of a particle is given by $4.0\hat{i} + 5.0t\hat{j}$ , then the magnitude of its acceleration (in $ms^{-2}$ ) is

A

4

B

-5

C

0

D

-4

E

5

Question 73: Palette 73/257

Errorless AMU (Med.) 2012 MCQ

One end of a string of length 1.0m is tied to a body of mass 0.5kg. It is whirled in a vertical circle with angular frequency 4 rad/s. The tension in the string when the body is at the lower most point of its motion will be equal to (Take $g = 10m/s^{2}$ )

A

3N

B

5N

C

8N

D

13N

Question 74: Palette 74/257

Errorless CBSE PMT (Pre.) 2012 MCQ

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

A

$\theta = \tan^{-1}\left(\frac{1}{4}\right)$

B

$\theta = \tan^{-1}(4)$

C

$\theta = \tan^{-1}(2)$

D

$\theta = 45^{\circ}$

Question 75: Palette 75/257

Errorless AIEEE 2012 MCQ

A boy can throw a stone up to a maximum height of 10m. The maximum horizontal distance that the boy can throw the same stone up to will be

A

$20\sqrt{2}m$

B

10m

C

$10\sqrt{2}m$

D

20m

Question 76: Palette 76/257

Errorless IIT-JEE 2012 MCQ

A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed $\omega$ . If the angular momentum of the system, calculated about O and P are denoted by $\vec{L}_{O}$ and $\vec{L}_{P}$ respectively, then

A

$\vec{L}_O$ and $\vec{L}_P$ do not vary with time

B

$\vec{L}_O$ varies with time while $\vec{L}_P$ remains constant

C

$\vec{L}_{O}$ remains constant while $\vec{L}_{P}$ varies with time

D

$\vec{L}_O$ and $\vec{L}_P$ both vary with time

Question 77: Palette 77/257

Errorless IIT JEE 2012 MCQ

Two identical discs of same radius $R$ are rotating about their axes in opposite directions with the same constant angular speed $\omega$ . The discs are in the same horizontal plane. At time $t = 0$ , the points $P$ and $Q$ are facing each other as shown in the figure. The relative speed between the two points $P$ and $Q$ is $V_r$ as function of times best represented by

A

B

C

D

Question 78: Palette 78/257

Errorless CBSE PMT (Pre.) 2011 MCQ

A particle moves in a circle of radius $5\mathrm{cm}$ with constant speed and time period $0.2\pi s$ . The acceleration of the particle is

A

$5m / s^2$

B

$15m / s^2$

C

$25m / s^2$

D

$36m / s^2$

Question 79: Palette 79/257

Errorless CBSE PMT (Mains) 2011 MCQ

A projectile is fired at an angle of $45^{\circ}$ with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is

A

$\tan^{-1}\left(\frac{\sqrt{3}}{2}\right)$

B

$45^{\circ}$

C

$60^{\circ}$

D

$\tan^{-1}\frac{1}{2}$

Question 80: Palette 80/257

Errorless Kerala PET 2011 MCQ

A particle crossing the origin of co-ordinates at time t=0, moves in the xy-plane with a constant acceleration a in the y-direction. If its equation of motion is $y=bx^{2}$ (b is a constant), its velocity component in the x-direction is

A

$\sqrt{\frac{2b}{a}}$

B

$\sqrt{\frac{a}{2b}}$

C

$\sqrt{\frac{a}{b}}$

D

$\sqrt{\frac{b}{a}}$

E

$\sqrt{ba}$

Question 81: Palette 81/257

Errorless Kerala PET 2011 MCQ

Two projectiles A and B thrown with speeds in the ratio $1:\sqrt{2}$ acquired the same heights. If A is thrown at an angle of $45^{\circ}$ with the horizontal, the angle of projection of B will be

A

$0^{\circ}$

B

$60^{\circ}$

C

$30^{\circ}$

D

$45^{\circ}$

E

$15^{\circ}$

Question 82: Palette 82/257

Errorless CBSE PMT (Pre.) 2011 MCQ

A missile is fired for maximum range with an initial velocity of 20 m/s. If $g = 10 \, m/s^{2}$ , the range of the missile is

A

20 m

B

40 m

C

50 m

D

60 m

Question 83: Palette 83/257

Errorless Odisha JEE 2010 MCQ

The earth moves round the sun in a near circular orbit of radius $1.5 \times 10^{11} m$ . Its centripetal acceleration is

A

$1.5 \times 10^{-3} m / s^2$

B

$3 \times 10^{-3} m / s^2$

C

$6 \times 10^{-3} m / s^2$

D

$12 \times 10^{-3} m / s^2$

Question 84: Palette 84/257

Errorless Kerala PMT 2010 MCQ

Centripetal acceleration is

A

A constant vector

B

A constant scalar

C

A magnitude changing vector

D

Not a constant vector

E

Time dependent scalar

Question 85: Palette 85/257

Errorless J & K CET 2010 MCQ

If a car is to travel with a speed v along the frictionless, banked circular track of radius r, the required angle of banking so that the car does skid is

A

$\theta = \tan^{-1}\left(\frac{v^{2}}{rg}\right)$

B

$\theta = \tan^{-1}\left(\frac{v}{rg}\right)$

C

$\theta = \tan^{-1}\left(\frac{r^{2}}{vg}\right)$

D

$\theta < \tan^{-1}\left(\frac{v^{2}}{rg}\right)$

Question 86: Palette 86/257

Errorless J & K CET 2010 MCQ

Which one of the following statements is not correct in uniform circular motion

A

The speed of the particle remains constant

B

The acceleration always points towards the centre

C

The angular speed remains constant

D

The velocity remains constant

Question 87: Palette 87/257

Errorless AIIMS 2010 MCQ

A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/sec. The tension in the string is 6 N, when the stone is at $(g = 10 \, m/sec^{2})$

A

Top of the circle

B

Bottom of the circle

C

Half way down

D

None of the above

Question 88: Palette 88/257

Errorless AMU (Med.) 2010 MCQ

A particle originally at rest at the highest point of a smooth vertical circle is slightly displaced. It will leave the circle at a vertical distance h below the highest point such that

A

$h = R$

B

$h = \frac {R}{3}$

C

$h = \frac {R}{2}$

D

$h = \frac {2 R}{3}$

Question 89: Palette 89/257

Errorless WB-JEE 2010 MCQ

A ball is projected horizontally with a velocity of 5 m/s from the top of a building 19.6 m high. How long will the ball take to hit the ground

A

$\sqrt{2}$ s

B

2 s

C

$\sqrt{3}$ s

D

3 s

Question 90: Palette 90/257

Errorless AIEEE 2010 MCQ

A small particle of mass m is projected at an angle $\theta$ with the x-axis with an initial velocity $v_{0}$ in the x-y plane as shown in the figure. At a time $t < \frac{v_{0} \sin \theta}{g}$ , the angular momentum of the particle is where $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along x, y and z-axis respectively

A

$\frac{1}{2} mgv_0t^2\cos \theta \hat{i}$

B

$-mgv_{0}t^{2}\cos \theta \hat{j}$

C

$mgv_{0}t\cos \theta \hat{k}$

D

$-\frac{1}{2} mgv_0t^2\cos \theta \hat{k}$

Question 91: Palette 91/257

Errorless J & K CET 2010 MCQ

An object is projected so that its horizontal range R is maximum. If the maximum height attained by the object is H, then the ratio of R/H is

A

4

B

1/4

C

2

D

1/2

Question 92: Palette 92/257

Errorless WB-JEE 2010 MCQ

A body is projected with a speed $u$ m/s at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $\frac{3}{4}th$ of the initial kinetic energy. The value of $\beta$ is

A

$30^{\circ}$

B

$45^{\circ}$

C

$60^{\circ}$

D

$120^{\circ}$

Question 93: Palette 93/257

Errorless CBSE PMT (Mains) 2010 MCQ

The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is

A

$60^{\circ}$

B

$15^{\circ}$

C

$30^{\circ}$

D

$45^{\circ}$

Question 94: Palette 94/257

Errorless AIEEE 2010; JEE (Main) 2019 MCQ

A particle is moving with velocity $\vec{v} = K(y\hat{i} + x\hat{j})$ , where $K$ is a constant. The general equation for its path is

A

$y^{2} = x^{2} + \text{constant}$

B

$y = x^{2} + \text{constant}$

C

$y^{2} = x + \text{constant}$

D

$xy = \text{constant}$

Question 95: Palette 95/257

Errorless AIEEE 2010 MCQ

A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of 'P' is such that it sweeps out a length $s = t^3 + 5$ , where $s$ is in metres and $t$ is in seconds. The radius of the path is $20\,m$ . The acceleration of 'P' when $t = 2\,s$ is nearly

A

$14m / s^2$

B

$13m / s^2$

C

$12m / s^2$

D

$7.2m / s^2$

Question 96: Palette 96/257

Errorless AIIMS 2010 MCQ

Assertion : A safe turn by a cyclist should neither be fast nor sharp. Reason : The bending angle from the vertical would decrease with increase in velocity.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 97: Palette 97/257

Errorless Kerala PET 2010 MCQ

A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity)

A

$\frac{4v^{2}}{5g}$

B

$\frac{4g}{5v^{2}}$

C

$\frac{v^{2}}{g}$

D

$\frac{4v^{2}}{\sqrt{5}g}$

Question 98: Palette 98/257

Errorless MP PMT 2009 MCQ

Which one is Angular resolution fundamental quantity

A

Length

B

Time

C

Radian

D

Angle

Question 99: Palette 99/257

Errorless DUMET 2009 MCQ

An object moves at a constant speed along a circular path in a horizontal XY plane, with the centre at the origin. When the object is at $x = -2m$ , its velocity is $-(4m / s)\hat{j}$ . What is the object's acceleration when it is $y = 2m$

A

$-(8m / s^2)\hat{j}$

B

$-(8m / s^2)\hat{i}$

C

$-(4m / s^2)\hat{j}$

D

$(4m / s^2)\hat{i}$

Question 100: Palette 100/257

Errorless MP PMT 2009 MCQ

Ratio between maximum range and square of time of flight in projectile motion is

A

10:49

B

49:10

C

98:10

D

10:98

Question 101: Palette 101/257

Errorless MP PMT 2009 MCQ

A body 'A' moves with constant velocity on a straight line path tangential to the earth's surface. Another body 'B' is thrown vertically upwards, it goes to a height and falls back on earth. A third body 'C' is projected to an angle and follows a parabolic path as shown in figure The bodies whose angular momentum relative to the center of the earth is conserved are

A

B only

B

B and C

C

A, B, C

D

None of the above

Question 102: Palette 102/257

Errorless EAMCET 2009 MCQ

A body is projected vertically upwards at time t = 0 and it is seen at a height H at instants $t_{1}$ and $t_{2}$ seconds during its flight. The maximum height attained is (g is acceleration due to gravity)

A

$\frac{g(t_{2}-t_{1})^{2}}{8}$

B

$\frac{g(t_{1}+t_{2})^{2}}{4}$

C

$\frac{g(t_{1}+t_{2})^{2}}{8}$

D

$\frac{g(t_{2}-t_{1})^{2}}{4}$

Question 103: Palette 103/257

Errorless Kerala PMT 2009 MCQ

The relation between the time of flight of a projectile $T_{f}$ and the time to reach the maximum height $t_{m}$ is

A

$T_{f}=2t_{m}$

B

$T_{f}=t_{m}$

C

$T_{f}=\frac{t_{m}}{2}$

D

$T_{f}=\sqrt{2}(t_{m})$

E

$T_{f}=\frac{t_{m}}{\sqrt{2}}$

Question 104: Palette 104/257

Errorless WB-JEE 2009 MCQ

A bullet is fired with a velocity $u$ making an angle of $60^{\circ}$ with the horizontal plane. The horizontal component of the velocity of the bullet when it reaches the maximum height is

A

$u$

B

0

C

$\frac{\sqrt{3u}}{2}$

D

$u / 2$

Question 105: Palette 105/257

Errorless DUMET 2009 MCQ

A coastguard ship locates a pirate ship at a distance 560 m. It fires a cannon ball with an initial speed 82 m/s. At what angle from horizontal the ball must be fired so that it hits the pirate ship

A

54°

B

125°

C

27°

D

18°

Question 106: Palette 106/257

Errorless IIT-JEE 2009 MCQ

A piece of wire is bent in the shape of a parabola $y = kx^{2}$ (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is

A

a/gk

B

a/2gk

C

2a/gk

D

a/4gk

Question 107: Palette 107/257

Errorless EAMCET 2009 MCQ

A particle is projected up from a point at an angle $\theta$ with the horizontal direction. At any time $t'$ , if $p$ is the linear momentum, $y$ is the vertical displacement, $x$ is horizontal displacement, the graph among the following which does not represent the variation of Kinetic energy $KE$ of the particle
(A)

(B)

(C)

(D)

A

Graph A

B

Graph B

C

Graph C

D

Graph D

Question 108: Palette 108/257

Errorless DUMET 2009 MCQ

Tom and Dick are running forward with the same speed. They are throwing a rubber ball to each other at a constant speed v as seen by the thrower. According to Sam who is standing on the ground the speed of the ball is

A

Same as v

B

Greater than v

C

Less than v

D

None of these

Question 109: Palette 109/257

Errorless Orissa JEE 2009 MCQ

A body is revolving with a uniform speed v in a circle of radius r. The tangential acceleration is

A

$\frac{v}{r}$

B

$\frac{v^{2}}{r}$

C

Zero

D

$\frac{v}{r^{2}}$

Question 110: Palette 110/257

Errorless CBSE PMT 2008 MCQ

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

A

16m/s and 17m/s

B

13m/s and 14m/s

C

14m/s and 15m/s

D

15m/s and 16m/s

Question 111: Palette 111/257

Errorless MP PET 2008 MCQ

A particle moves in a circle of radius 30 cm. Its linear speed is given by v = 2t where t in second and v in m/s. Find out its radial and tangential acceleration at t = 3 sec respectively,

A

$220m/sec^{2}, 50m/sec^{2}$

B

$100m/sec^{2}, 5m/sec^{2}$

C

$120m/sec^{2}, 2m/sec^{2}$

D

$110m/sec^{2}, 10m/sec^{2}$

Question 112: Palette 112/257

Errorless J & K CET 2008; MP PET 2013 MCQ

A body moving along a circular path of radius $R$ with velocity $v$ , has centripetal acceleration $a$ . If its velocity is made equal to $2v$ , then its centripetal acceleration is

A

$4a$

B

$2a$

C

$\frac{a}{4}$

D

$\frac{a}{2}$

Question 113: Palette 113/257

Errorless MP PET 2008 MCQ

A projectile moves from the ground such that its horizontal displacement is $x = Kt$ and vertical displacement is $y = Kt(1 - \alpha t)$ , where $K$ and $\alpha$ are constants and $t$ is time. Find out total time of flight (T) and maximum height attained ( $Y_{\max}$ ) its

A

$T = \alpha$ , $Y_{\max} = \frac{K}{2\alpha}$

B

$T = \frac{1}{\alpha}$ , $Y_{\max} = \frac{2K}{\alpha}$

C

$T = \frac{1}{\alpha}$ , $Y_{\max} = \frac{K}{6\alpha}$

D

$T = \frac{1}{\alpha}$ , $Y_{\max} = \frac{K}{4\alpha}$

Question 114: Palette 114/257

Errorless MP PET 2008; JEE (Main) 2021 MCQ

A particle is projected with velocity $V_{0}$ along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e. $a=\alpha x^{2}$ , the distance at which the particle stops is

A

$\sqrt{\frac{3V_{0}}{2\alpha}}$

B

$\left(\frac{3V_{0}}{2\alpha}\right)^{\frac{1}{3}}$

C

$\sqrt{\frac{2V_{0}^{2}}{3\alpha}}$

D

$\left(\frac{3V_{0}^{2}}{2\alpha}\right)^{\frac{1}{3}}$

Question 115: Palette 115/257

Errorless Odisha JEE 2008 MCQ

A body is fired vertically upward. At half the maximum height, the velocity of the body is 10 m/s. The maximum height raised by the body is

A

0 m

B

10 m

C

15 m

D

20 m

Question 116: Palette 116/257

Errorless Odisha JEE 2008 MCQ

A body is thrown upward from the earth surface with velocity 5 m/s and from a planet surface with velocity 3 m/s. Both follow the same path. What is the projectile acceleration due to gravity on the planet

A

$2 \, m/s^{2}$

B

$3.5 \, m/s^{2}$

C

$4 \, m/s^{2}$

D

$5 \, m/s^{2}$

Question 117: Palette 117/257

Errorless Kerala PET 2008 MCQ

Two particles A and B are projected with same speed so that the ratio of their maximum heights reached is 3:1. If the speed of A is doubled without altering other parameters, the ratio of the horizontal ranges attained by A and B is

A

1:1

B

2:1

C

4:1

D

3:2

E

4:3

Question 118: Palette 118/257

Errorless IIT-JEE 2008 MCQ

A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle $\theta$ at which the speed of the bob is half of that at A, satisfies

A

$\theta = \frac{\pi}{4}$

B

$\frac{\pi}{4} < \theta < \frac{\pi}{4}$

C

$\frac{\pi}{2} < \theta < \frac{3\pi}{4}$

D

$\frac{3\pi}{4} < \theta < \pi$

Question 119: Palette 119/257

Errorless AIIMS 2008 MCQ

Assertion : A body of mass 1 kg is making 1 rps in a circle of radius 1 m. centrifugal force acting on it is $4\pi^{2}N$ . Reason : Centrifugal force is given by $F = \frac{mv^{2}}{r}$

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 120: Palette 120/257

Errorless Kerala PMT 2008 MCQ

In uniform circular motion of a particle

A

Velocity is constant but acceleration is variable

B

Velocity is variable but acceleration in constant

C

Both speed and acceleration are constant

D

Speed is constant but acceleration is variable

E

Both speed and acceleration are variable

Question 121: Palette 121/257

Errorless CBSE PMT 2008 MCQ

A body of mass m is projected at an angle of $45^{\circ}$ with the horizontal. If air resistance is negligible, then total change in momentum when it strikes the ground is

A

2mv

B

$\sqrt{2}$ mv

C

mv

D

$mv/\sqrt{2}$

Question 122: Palette 122/257

Errorless MP PET 2007 MCQ

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity $\omega_{0}$ . If the length of the string and angular velocity both are doubled, the tension in the string which was initially $T_{0}$ is now

A

$T_{0}$

B

$T_{0}/2$

C

$4T_{0}$

D

$8T_{0}$

Question 123: Palette 123/257

Errorless MP PET 2007; AIEEE 2011 MCQ

A large number of bullets are fired in all directions with same speed v. What is the maximum area on the ground on which these bullets will spread

A

$\pi\frac{v^{2}}{g}$

B

$\pi\frac{v^{4}}{g^{2}}$

C

$\pi^{2}\frac{v^{4}}{g^{2}}$

D

$\pi^{2}\frac{v^{2}}{g^{2}}$

Question 124: Palette 124/257

Errorless Kerala PET 2007 MCQ

A ball is projected from the ground at a speed of $10ms^{-1}$ making an angle of $30^{\circ}$ with the horizontal. Another ball is simultaneously released from a point on the vertical line along the maximum height of the projectile. Both the balls collide at the maximum height of first ball. The initial height of the second ball is $(g=10ms^{-2})$

A

6.25m

B

2.5m

C

3.75m

D

5m

Question 125: Palette 125/257

Errorless Kerala PMT 2007 MCQ

A particle is projected with a speed v at $45^{\circ}$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is

A

Zero

B

$\frac{mvh^{2}}{\sqrt{2}}$

C

$\frac{mvh}{\sqrt{2}}$

D

$\frac{mvh^{3}}{\sqrt{2}}$

Question 126: Palette 126/257

Errorless AIIMS 2007 MCQ

A particle is thrown above, then correct $v - t$ graph will be

A

B

C

D

Question 127: Palette 127/257

Errorless BHU 2006; AMU 2010; NEET 2017 MCQ

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$ , the net force on the particle (directed towards the centre) will be ( $T$ represents the tension in the string)

A

$T$

B

$T - \frac{mv^2}{l}$

C

$T + \frac{mv^2}{l}$

D

Zero

Question 128: Palette 128/257

Errorless RPMT 2006 MCQ

A body is moving in a circular path with acceleration $a$ . If its velocity gets doubled, find the ratio of acceleration after and before the change

A

$1:4$

B

$\frac{1}{4}:2$

C

$2:1$

D

$4:1$

Question 129: Palette 129/257

Errorless CBSE PMT 2006 MCQ

A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular loop. The average velocity and average speed for each circular loop respectively is

A

10 m/s, 10 m/s

B

10 m/s, 0

C

0, 0

D

0, 10 m/s

Question 130: Palette 130/257

Errorless J & K CET 2006 MCQ

Two particles of equal mass are connected to a rope AB of negligible mass such that one is at end A and other dividing the length of rope in the ratio 1:2 from B. The rope is rotated about end B in a horizontal plane. Ratio of tensions in the smaller part to the other is (ignore effect of gravity)

A

4:3

B

1:4

C

1:2

D

1:3

Question 131: Palette 131/257

Errorless BHU 2006 MCQ

A cart is moving horizontally along a straight line with constant speed 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80m. At what speed (relative to the cart) must the projectile be fired (Take $g = 10m/s^{2}$ )

A

10 m/s

B

$10\sqrt{8}$ m/s

C

$\frac{40}{3}$ m/s

D

None of these

Question 132: Palette 132/257

Errorless CBSE PMT 2006 MCQ

Galileo writes that for angles of projection of a projectile at angles $(45^{\circ} + \theta)$ and $(45^{\circ} - \theta)$ , the horizontal ranges described by the projectile are in the ratio of (if $\theta \leq 45^{\circ}$ )

A

2:1

B

1:2

C

1:1

D

2:3

Question 133: Palette 133/257

Errorless MP PMT 2006 MCQ

An arrow is shot into air. Its range is 200 m and its time of flight is 5 s. If $g = 10 \, m/s^{2}$ , then the horizontal component of velocity of the arrow is

A

12.5 m/s

B

25 m/s

C

31.25 m/s

D

40 m/s

Question 134: Palette 134/257

Errorless J & K CET 2006 MCQ

Two bodies are projected from ground with equal speeds 20 m/sec from the same position in same vertical plane to have equal range but at different angle above the horizontal. If one of the angle is $30^{\circ}$ the sum of their maximum heights is (assume $g = 10m/s^{2}$ )

A

400 m

B

20 m

C

30 m

D

40 m

Question 135: Palette 135/257

Errorless BCECE 2006 MCQ

A projectile is projected with $a$ speed $u$ making an angle $2\theta$ with the horizontal. what is the speed when its direction of motion makes an angle $\theta$ with the horizontal

A

$(u\cos 2\theta) / 2$

B

$u\cos \theta$

C

$u(2\cos \theta -\sec \theta)$

D

$u(\cos \theta -\sec \theta)$

Question 136: Palette 136/257

Errorless UP CPMT 2006 MCQ

A ball is thrown up at an angle with the horizontal. Then the total change of momentum by the instant it returns to ground is

A

Acceleration due to gravity $\times$ total time of flight

B

Weight of the ball $\times$ half the time of flight

C

Weight of the ball $\times$ total time of flight

D

Weight of the ball $\times$ horizontal range

Question 137: Palette 137/257

Errorless AFMC 2006 MCQ

A projectile is thrown in the upward direction making an angle of $60^{\circ}$ with the horizontal direction with a velocity of $147~\mathrm{ms^{-1}}$ . Then the time after which its inclination with the horizontal is $45^{\circ}$ , is

A

$15~s$

B

$10.98~s$

C

$5.49~s$

D

$2.745~s$

Question 138: Palette 138/257

Errorless CBSE PMT 2006; DCE 2006 MCQ

A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega$ . The force exerted by the liquid at the other end is

A

$\frac{ML\omega^{2}}{2}$

B

$ML\omega^{2}$

C

$\frac{ML\omega^{2}}{4}$

D

$\frac{ML^{2}\omega^{2}}{2}$

Question 139: Palette 139/257

Errorless UP CPMT 2006 MCQ

The angular amplitude of a simple pendulum is $\theta_0$ . The maximum tension in its string will be

A

$mg(1 - \theta_0)$

B

$mg(1 + \theta_0)$

C

$mg(1 - \theta_0^2)$

D

$mg(1 + \theta_0^2)$

Question 140: Palette 140/257

Errorless Kerala PMT 2006 MCQ

Consider the given velocity-time graph It represents the motion of

A

A projectile projected vertically upward, from a point

B

An electron in the hydrogen atom

C

A car with constant acceleration along a straight road

D

A bullet fired horizontally from the top of a tower

Question 141: Palette 141/257

Errorless Kerala PET 2005 MCQ

If the length of the second's hand in a stop clock is 3 cm the angular velocity and linear velocity of the tip is

A

0.2047 rad/sec., 0.0314 m/sec

B

0.2547 rad/sec., 0.314 m/sec

C

0.1472 rad/sec., 0.06314 m/sec

D

0.1047 rad/sec., 0.00314 m/sec

Question 142: Palette 142/257

Errorless Odisha JEE 2005 MCQ

What is the angular velocity of earth

A

$\frac{2\pi}{86400}\mathrm{rad / sec}$

B

$\frac{2\pi}{3600}\mathrm{rad / sec}$

C

$\frac{2\pi}{24}\mathrm{rad / sec}$

D

$\frac{2\pi}{6400}\mathrm{rad / sec}$

Question 143: Palette 143/257

Errorless J & K CET 2005 MCQ

A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of 0.5 m/s. What is the height of the plane of circle from vertex of the funnel

A

0.25 cm

B

2 cm

C

4 cm

D

2.5 cm

Question 144: Palette 144/257

Errorless CBSE PMT 2005 MCQ

A stone tied to the end of a string $1m$ long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolution in 44 seconds, what is the magnitude and direction of acceleration of the stone

A

$\pi^2 / 4ms^{-2}$ and direction along the radius towards the centre

B

$\pi^2 ms^{-2}$ and direction along the radius away from the centre

C

$\pi^2 ms^{-2}$ and direction along the radius towards the centre

D

$\pi^2 ms^{-2}$ and direction along the tangent to the circle

Question 145: Palette 145/257

Errorless BCECE 2005 MCQ

A particle is moving in a circle of radius R with constant speed v, if radius is double then its centripetal force to keep the same speed should be

A

Doubled

B

Halved

C

Quadrupled

D

Unchanged

Question 146: Palette 146/257

Errorless Odisha JEE 2005 MCQ

The angle turned by a body undergoing circular motion depends on time as $\theta = \theta_0 + \theta_1 t + \theta_2 t^2$ . Then the angular acceleration of the body is

A

$\theta_1$

B

$\theta_2$

C

$2\theta_1$

D

$2\theta_2$

Question 147: Palette 147/257

Errorless IIT JEE 2005 MCQ

A particle moves in a circular path with decreasing speed. Choose the correct statement

A

Angular momentum remains constant

B

Acceleration $(\vec{a})$ is towards the centre

C

Particle moves in a spiral path with decreasing radius

D

The direction of angular momentum remains constant

Question 148: Palette 148/257

Errorless Odisha JEE 2005; DCE 2006 MCQ

Three particles A, B and C are thrown from the top of a tower with the same speed. A is thrown up, B is thrown down and C is horizontally. They hit the ground with speeds $V_{A}$ , $V_{B}$ and $V_{C}$ respectively

A

$V_{A} = V_{B} = V_{C}$

B

$V_{A} = V_{B} > V_{C}$

C

$V_{B} > V_{C} > V_{A}$

D

$V_{A} > V_{B} = V_{C}$

Question 149: Palette 149/257

Errorless RPMT 2005; Kerala PET 2009 MCQ

A bullet is to be fired with a speed of $2000 \, ms^{-1}$ to hit a target 200 m away on a level ground. If $g = 10 \, ms^{-2}$ , the gun should be aimed

A

Directly at the target

B

5 cm below the target

C

5 cm above the target

D

2 cm above the target

E

2 cm below the target

Question 150: Palette 150/257

Errorless RPMT 2005 MCQ

A projectile fired with initial velocity u at some angle $\theta$ has a range R. If the initial velocity be doubled at the same angle of projection, then the range will be

A

2R

B

R/2

C

R

D

4R

Question 151: Palette 151/257

Errorless RPMT 2005 MCQ

If retardation produced by air resistance of projectile is one-tenth of acceleration due to gravity, the time to reach maximum height

A

Decreases by 11 percent

B

Increases by 11 percent

C

Decreases by 9 percent

D

Increases by 9 percent

Question 152: Palette 152/257

Errorless DPMT 2005 MCQ

Two bodies are thrown up at angles of $45^{\circ}$ and $60^{\circ}$ , respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is

A

$\sqrt{\frac{2}{3}}$

B

$\frac{2}{\sqrt{3}}$

C

$\sqrt{\frac{3}{2}}$

D

$\frac{\sqrt{3}}{2}$

Question 153: Palette 153/257

Errorless Odisha JEE 2005 MCQ

At what point of a projectile motion acceleration and velocity are perpendicular to each other

A

At the point of projection

B

At the point of drop

C

At the topmost point

D

Any where in between the point of projection and topmost point

Question 154: Palette 154/257

Errorless AFMC 2005 MCQ

The maximum horizontal range of a projectile is $400m$ . The maximum value of height attained by it will be

A

$100m$

B

$200m$

C

$400m$

D

$800m$

Question 155: Palette 155/257

Errorless Kerala PMT 2004 MCQ

Two particles of equal masses are revolving in circular paths of radii $r_1$ and $r_2$ respectively with the same speed. The ratio of their centripetal forces is

A

$\frac{r_2}{r_1}$

B

$\sqrt{\frac{r_2}{r_1}}$

C

$\left(\frac{r_1}{r_2}\right)^2$

D

$\left(\frac{r_2}{r_1}\right)^2$

Question 156: Palette 156/257

Errorless KCET 2004 MCQ

When a body moves in a circular path, no work is done by the force since,

A

There is no displacement

B

There is no net force

C

Force and displacement are perpendicular to each other

D

The force is always away from the centre

Question 157: Palette 157/257

Errorless AIEEE 2004 MCQ

Which of the following statements is false for a particle moving in a circle with a constant angular speed

A

The velocity vector is tangent to the circle

B

The acceleration vector is tangent to the circle

C

The acceleration vector points to the centre of the circle

D

The velocity and acceleration vectors are perpendicular to each other

Question 158: Palette 158/257

Errorless DCE 2004 MCQ

An object is moving in a circle of radius 100 m with a constant speed of 31.4 m/s. What is its average speed for one complete revolution

A

Zero

B

31.4 m/s

C

3.14 m/s

D

$\sqrt{2} \times 31.4$ m/s

Question 159: Palette 159/257

Errorless CPMT 2004; RPMT 2006 MCQ

If $a_r$ and $a_t$ represent radial and tangential accelerations, the motion of a particle will be uniformly circular if

A

$a_r = 0$ and $a_t = 0$

B

$a_r = 0$ but $a_t \neq 0$

C

$a_r \neq 0$ but $a_t = 0$

D

$a_r \neq 0$ and $a_t \neq 0$

Question 160: Palette 160/257

Errorless DPMT 2004 MCQ

Figure shows a body of mass $m$ moving with a uniform speed $v$ along a circle of radius $r$ . The change in velocity in going from $A$ to $B$ is

A

$v \sqrt {2}$

B

$v / \sqrt {2}$

C

v

D

Zero

Question 161: Palette 161/257

Errorless MP PMT 2004 MCQ

A particle moves in a plane with constant acceleration in a direction different from the initial velocity. The path of the particle will be

A

A straight line

B

An arc of a circle

C

A parabola

D

An ellipse

Question 162: Palette 162/257

Errorless BCECE 2004 MCQ

At the height 80 m, an aeroplane is moving with 150 m/s. A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped (Given $g = 10 \, m/s^{2}$ )

A

605.3 m

B

600 m

C

80 m

D

230 m

Question 163: Palette 163/257

Errorless MP PMT 2004 MCQ

A ball is projected with velocity $V_{o}$ at an angle of elevation 30°. Mark the correct statement

A

Kinetic energy will be zero at the highest point of the trajectory

B

Vertical component of momentum will be conserved

C

Horizontal component of momentum will be conserved

D

Gravitational potential energy will be minimum at the highest point of the trajectory

Question 164: Palette 164/257

Errorless J & K CET 2004 MCQ

Neglecting the air resistance, the time of flight of a projectile is determined by

A

$U_{\text{vertical}}$

B

$U_{\text{horizontal}}$

C

$U = U^{2}_{\text{vertical}} + U^{2}_{\text{horizontal}}$

D

$U = U(U^{2}_{\text{vertical}} + U^{2}_{\text{horizontal}})^{1/2}$

Question 165: Palette 165/257

Errorless AIEEE 2004 MCQ

A ball is thrown from a point with a speed $v_{o}$ at an angle of projection $\theta$ . From the same point and at the same instant a person starts running with a constant speed $v_{o} / 2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection

A

Yes, $60^{\circ}$

B

Yes, $30^{\circ}$

C

No

D

Yes, $45^{\circ}$

Question 166: Palette 166/257

Errorless BCECE 2004 MCQ

A stone is thrown at an angle $\theta$ to the horizontal reaches a maximum height $H$ . Then the time of flight of stone will be

A

$\sqrt{\frac{2H}{g}}$

B

$2\sqrt{\frac{2H}{g}}$

C

$\frac{2\sqrt{2H\sin\theta}}{g}$

D

$\frac{\sqrt{2H\sin\theta}}{g}$

Question 167: Palette 167/257

Errorless DPMT 2004 MCQ

A ball is projected upwards from the top of tower with a velocity $50 \, ms^{-1}$ making an angle $30^{\circ}$ with the horizontal. The height of tower is 70 m. After how many seconds from the instant of throwing will the ball reach the ground

A

2 s

B

5 s

C

7 s

D

9 s

Question 168: Palette 168/257

Errorless MP PET 2003, 13 MCQ

A body of mass $m$ moves in a circular path with uniform angular velocity. The motion of the body has constant

A

Acceleration

B

Velocity

C

Momentum

D

Kinetic energy

Question 169: Palette 169/257

Errorless UPSEAT 2003 MCQ

Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is $v_{0}$ , then the ratio of tensions in the three sections of the string is

A

3:5:7

B

3:4:5

C

7:11:6

D

3:5:6

Question 170: Palette 170/257

Errorless MP PMT 2003 MCQ

A car sometimes overturns while taking a turn. When it overturns, it is

A

The inner wheel which leaves the ground first

B

The outer wheel which leaves the ground first

C

Both the wheels leave the ground simultaneously

D

Either wheel leaves the ground first

Question 171: Palette 171/257

Errorless RPET 2003 MCQ

A particle is moving on a circular path with constant speed, then its acceleration will be

A

Zero

B

External radial acceleration

C

Internal radial acceleration

D

Constant acceleration

Question 172: Palette 172/257

Errorless MP PMT 2003 MCQ

The length of second's hand in a watch is 1 cm. The change in velocity of its tip in 15 seconds is

A

Zero

B

$\frac{\pi}{30\sqrt{2}}$ cm/sec

C

$\frac{\pi}{30}$ cm/sec

D

$\frac{\pi\sqrt{2}}{30}$ cm/sec

Question 173: Palette 173/257

Errorless AFMC 2003 MCQ

The force required to keep a body in uniform circular motion is

A

Centripetal force

B

Centrifugal force

C

Resistance

D

None of the above

Question 174: Palette 174/257

Errorless Pb. PET 2003; MP PET 2010 MCQ

The acceleration of a train travelling with speed of 400 m/s as it goes round a curve of radius 160 m, is

A

$1 \, km/s^{2}$

B

$100 \, m/s^{2}$

C

$10 \, m/s^{2}$

D

$1 \, m/s^{2}$

Question 175: Palette 175/257

Errorless DPMT 2003 MCQ

A body of mass 1 kg tied to one end of string is revolved in a horizontal circle of radius 0.1 m with a speed of 3 revolution/sec, assuming the effect of gravity is negligible, then linear velocity, acceleration and tension in the string will be

A

1.88 m/s, 35.5 m/s², 35.5 N

B

2.88 m/s, 45.5 m/s², 45.5 N

C

3.88 m/s, 55.5 m/s², 55.5 N

D

None of these

Question 176: Palette 176/257

Errorless Odisha JEE 2003 MCQ

A particle of mass $M$ is moving in a horizontal circle of radius $R$ with uniform speed $V$ . When it moves from one point to a diametrically opposite point, its

A

Kinetic energy changes by $MV^2 / 4$

B

Momentum does not change

C

Momentum changes by $2MV$

D

Kinetic energy changes by $MV^2$

Question 177: Palette 177/257

Errorless Pb. PET 2003 MCQ

The maximum and minimum tension in the string whirling in a circle of radius $2.5m$ with constant velocity are in the ratio 5:3 then its velocity is

A

$\sqrt{98} m / s$

B

$7m / s$

C

$\sqrt{490} m / s$

D

$\sqrt{4.9}$

Question 178: Palette 178/257

Errorless BHU 2003 MCQ

A particle is kept at rest at the top of a sphere of diameter 42 m. When disturbed slightly, it slides down. At what height 'h' from the bottom, the particle will leave the sphere

A

14 m

B

28 m

C

35 m

D

7 m

Question 179: Palette 179/257

Errorless MH CET 2003 MCQ

A bomber plane moves horizontally with a speed of 500 m/s and a bomb released from it, strikes the ground in 10 sec. Angle at which it strikes the ground will be $(g = 10 \, \text{m/s}^2)$

A

$\tan^{-1}\left(\frac{1}{5}\right)$

B

$\tan^{-1}\left(\frac{1}{2}\right)$

C

$\tan^{-1}(1)$

D

$\tan^{-1}(5)$

Question 180: Palette 180/257

Errorless BVP 2003 MCQ

A cricketer hits a ball with a velocity 25 m/s at $60^{\circ}$ above the horizontal. How far above the ground it passes over a fielder 50 m from the bat (assume the ball is struck very close to the ground)

A

8.2 m

B

9.0 m

C

11.6 m

D

12.7 m

Question 181: Palette 181/257

Errorless EAMCET 2003 MCQ

The equation of motion of a projectile are given by $x = 36t$ metre and $2y = 96t - 9.8t^2$ metre. The angle of projection is

A

$\sin^{-1}\left(\frac{4}{5}\right)$

B

$\sin^{-1}\left(\frac{3}{5}\right)$

C

$\sin^{-1}\left(\frac{4}{3}\right)$

D

$\sin^{-1}\left(\frac{3}{4}\right)$

Question 182: Palette 182/257

Errorless KCET 2003; AIEEE 2004; AIIMS 2008; DCE 2009 MCQ

For a given velocity, a projectile has the same range R for two angles of projection if $t_{1}$ and $t_{2}$ are the times of flight in the two cases then

A

$t_{1}t_{2} \propto R^{2}$

B

$t_{1}t_{2} \propto R$

C

$t_{1}t_{2} \propto \frac{1}{R}$

D

$t_{1}t_{2} \propto \frac{1}{R^{2}}$

Question 183: Palette 183/257

Errorless DPMT 2003; J & K CET 2004 MCQ

The horizontal range of a projectile is $4\sqrt{3}$ times its maximum height. Its angle of projection will be

A

$45^{\circ}$

B

$60^{\circ}$

C

$90^{\circ}$

D

$30^{\circ}$

Question 184: Palette 184/257

Errorless AFMC 2002, 03 MCQ

A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to overturn is

A

Doubled

B

Quadrupled

C

Halved

D

Unchanged

Question 185: Palette 185/257

Errorless Kerala (Med.) 2002 MCQ

A proton of mass $1.6 \times 10^{-27}$ kg goes round in a circular orbit of radius 0.10 m under a centripetal force of $4 \times 10^{-13}$ N. then the frequency of revolution of the proton is about

A

$0.08 \times 10^{8}$ cycles per sec

B

$4 \times 10^{8}$ cycles per sec

C

$8 \times 10^{8}$ cycles per sec

D

$12 \times 10^{8}$ cycles per sec

Question 186: Palette 186/257

Errorless Kerala (Med.) 2002 MCQ

An athlete completes one round of a circular track of radius 10 m in 40 sec. The distance covered by him in 2 min 20 sec is

A

70 m

B

140 m

C

110 m

D

220 m

Question 187: Palette 187/257

Errorless AFMC 2002 MCQ

A car is moving with high velocity when it has a turn. A force acts on it outwardly because of

A

Centripetal force

B

Centrifugal force

C

Gravitational force

D

All the above

Question 188: Palette 188/257

Errorless Odisha JEE 2002 MCQ

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is

A

$2\pi v/T$

B

$2\pi r/T$

C

$2\pi r^{2}/T$

D

$2\pi v^{2}/T$

Question 189: Palette 189/257

Errorless MP PET 2002 MCQ

In an atom for the electron to revolve around the nucleus, the necessary centripetal force is obtained from the following force exerted by the nucleus on the electron

A

Nuclear force

B

Gravitational force

C

Magnetic force

D

Electrostatic force

Question 190: Palette 190/257

Errorless MP PMT 2002 MCQ

A particle of mass m moves with constant speed along a circular path of radius r under the action of a force F. Its speed is

A

$\sqrt{\frac{rF}{m}}$

B

$\sqrt{\frac{F}{r}}$

C

$\sqrt{Fmr}$

D

$\sqrt{\frac{F}{mr}}$

Question 191: Palette 191/257

Errorless Odisha JEE 2002 MCQ

A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles $30^{\circ}$ and $60^{\circ}$ from vertical (lowest position) are $T_{1}$ and $T_{2}$ respectively. then

A

$T_{1} = T_{2}$

B

$T_{2} > T_{1}$

C

$T_{1} > T_{2}$

D

Tension in the string always remains the same

Question 192: Palette 192/257

Errorless Odisha JEE 2002 MCQ

A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum displacement of the pendulum with respect to the vertical

A

$30^{\circ}$

B

$45^{\circ}$

C

$60^{\circ}$

D

$90^{\circ}$

Question 193: Palette 193/257

Errorless MH CET 2002 MCQ

A body crosses the topmost point of a vertical circle with critical speed. Its centripetal acceleration, when the string is horizontal will be

A

$6g$

B

$3g$

C

$2g$

D

$g$

Question 194: Palette 194/257

Errorless CBSE PMT 2002; Odisha JEE 2003 MCQ

A particle (A) is dropped from a height and another particle (B) is thrown in horizontal direction with speed of 5 m/sec from the same height. The correct statement is

A

Both particles will reach at ground simultaneously

B

Both particles will reach at ground with same speed

C

Particle (A) will reach at ground first with respect to particle (B)

D

Particle (B) will reach at ground first with respect to particle (A)

Question 195: Palette 195/257

Errorless Pb. PMT 2002 MCQ

A ball thrown by one player reaches the other in 2 sec. the maximum height attained by the ball above the point of projection will be about

A

$10m$

B

$7.5m$

C

$5m$

D

$2.5m$

Question 196: Palette 196/257

Errorless AIEEE 2002 MCQ

In a projectile motion, velocity at maximum height is

A

$\frac{u\cos\theta}{2}$

B

$u\cos\theta$

C

$\frac{u\sin\theta}{2}$

D

None of these

Question 197: Palette 197/257

Errorless UPSEAT 2002 MCQ

A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is

A

100 m

B

80 m

C

60 m

D

50 m

Question 198: Palette 198/257

Errorless BHU 2002; DPMT 2004 MCQ

A string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $2 / \pi$ revolutions per second around the vertical axis through the fixed end as shown in the figure, then tension in the string is

A

ML

B

2ML

C

4ML

D

16 ML

Question 199: Palette 199/257

Errorless IIT-JEE (Screening) 2002 MCQ

A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector $\vec{a}$ is correctly shown in

A

B

C

D

Question 200: Palette 200/257

Errorless Kerala (Engg.) 2001; MP PMT 2009 MCQ

A cyclist riding the bicycle at a speed of $14\sqrt{3}$ ms $^{-1}$ takes a turn around a circular road of radius $20\sqrt{3}$ m without skidding. Given $g = 9.8 \, ms^{-2}$ , what is his inclination to the vertical

A

$30^{\circ}$

B

$90^{\circ}$

C

$45^{\circ}$

D

$60^{\circ}$

Question 201: Palette 201/257

Errorless KCET 2001; Kerala PMT 2008 MCQ

When a ceiling fan is switched off its angular velocity reduces to $50\%$ while it makes 36 rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation)

A

18

B

12

C

36

D

48

Question 202: Palette 202/257

Errorless CPMT 2001 MCQ

A coin, placed on a rotating turn-table slips, when it is placed at a distance of 9 cm from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is

A

27 cm

B

9 cm

C

3 cm

D

1 cm

Question 203: Palette 203/257

Errorless MP PET 2001; Pb. PET 2004 MCQ

A particle of mass m is projected with velocity v making an angle of $45^{\circ}$ with the horizontal. The magnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height is (where g = acceleration due to gravity)

A

Zero

B

$mv^{3}/(4\sqrt{2}g)$

C

$mv^{3}/(\sqrt{2}g)$

D

$mv^{2}/2g$

Question 204: Palette 204/257

Errorless KCET 2001; JIPMER 2001, 02 MCQ

A body is thrown with a velocity of 9.8 m/s making an angle of $30^{\circ}$ with the horizontal. It will hit the ground after a time

A

1.5 s

B

1 s

C

3 s

D

2 s

Question 205: Palette 205/257

Errorless CBSE PMT 2001; AIEEE 2007 MCQ

A projectile is projected with kinetic energy $K$ . If it has the maximum possible horizontal range, then its kinetic energy at the highest point will be

A

$0.25K$

B

$0.5K$

C

$0.75K$

D

$1.0K$

Question 206: Palette 206/257

Errorless AMU (Med.) 2001 MCQ

A batsman hits a sixer and the ball touches the ground outside the cricket ground. Which of the following graph describes the variation of the cricket ball's vertical velocity v with time between the time $t_{1}$ as it hits the bat and time $t_{2}$ when it touches the ground

A

B

C

D

Question 207: Palette 207/257

Errorless Pb. PET 2000, 01; J & K CET 2006 MCQ

A motor cyclist moving with a velocity of 72 km/hour on a flat road takes a turn on the road at a point where the radius of curvature of the road is 20 m. The acceleration due to gravity is $10 \, m/sec^{2}$ . In order to avoid skidding, he must not bend with respect to the vertical plane by an angle greater than

A

$\theta = \tan^{-1} 6$

B

$\theta = \tan^{-1} 2$

C

$\theta = \tan^{-1} 25.92$

D

$\theta = \tan^{-1} 4$

Question 208: Palette 208/257

Errorless DCE 2000, 01, 03 MCQ

In uniform circular motion, the velocity vector and acceleration vector are

A

Perpendicular to each other

B

Same direction

C

Opposite direction

D

Not related to each other

Question 209: Palette 209/257

Errorless CBSE PMT 2000; JIPMER 2002 MCQ

If a body A of mass M is thrown with velocity V at an angle of $30^{\circ}$ to the horizontal and another body B of the same mass is thrown with the same speed at an angle of $60^{\circ}$ to the horizontal. The ratio of horizontal range of A to B will be

A

1:3

B

1:1

C

$1:\sqrt{3}$

D

$\sqrt{3}:1$

Question 210: Palette 210/257

Errorless RPMT 2000 MCQ

A particle covers 50 m distance when projected with an initial speed. On the same surface it will cover a distance, when projected with double the initial speed

A

100 m

B

150 m

C

200 m

D

250 m

Question 211: Palette 211/257

Errorless 2000 MCQ

A bullet is fired from a gun at the speed of $280 \, ms^{-1}$ in the direction $30^{\circ}$ above the horizontal. The maximum height attained by the bullet is $(g = 9.8 \, \text{ms}^{-2}, \sin 30^{\circ} = 0.5)$

A

2000 m

B

1000 m

C

3000 m

D

2800 m

Question 212: Palette 212/257

Errorless RPET 1999; Odisha PMT 2004; MP PET 2008, 09 MCQ

A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is $\frac{mv^{2}}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle

A

$\frac{mv^{2}}{r} \times \pi r$

B

Zero

C

$\frac{mv^{2}}{r^{2}}$

D

$\frac{\pi r^{2}}{mv^{2}}$

Question 213: Palette 213/257

Errorless RPET 1999; DCE 2009; Kerala PMT 2009 MCQ

A body is tided with a string and is given a circular motion with velocity v in radius r. The magnitude of the acceleration is

A

$\frac{v}{r}$

B

$\frac{v^{2}}{r}$

C

$\frac{v}{r^{2}}$

D

$\frac{v^{2}}{r^{2}}$

Question 214: Palette 214/257

Errorless UPSEAT 1999; MP PMT 2012 MCQ

A particle revolves round a circular path. The acceleration of the particle is

A

Along the circumference of the circle

B

Along the tangent

C

Along the radius

D

Zero

Question 215: Palette 215/257

Errorless DPMT 1999; UPSEAT 2000; RPET 2003; Pb. PET 2004; CBSE PMT (Pre.) 2011 MCQ

A particle moves in a circle of radius 25 cm at two revolutions per second. The acceleration of the particle in $m/s^{2}$ is

A

$\pi^{2}$

B

$8\pi^{2}$

C

$4\pi^{2}$

D

$2\pi^{2}$

Question 216: Palette 216/257

Errorless MP PMT 1999; Kerala PET 2010 MCQ

A string breaks if its tension exceeds 10 newtons. A stone of mass $250\mathrm{gm}$ tied to this string of length $10~cm$ is rotated in a horizontal circle. The maximum angular velocity of rotation can be

A

$20\mathrm{rad / s}$

B

$40\mathrm{rad / s}$

C

$100\mathrm{rad / s}$

D

$200\mathrm{rad / s}$

Question 217: Palette 217/257

Errorless CBSE PMT 1999; KCET 2001; JIPMER 2001. 02; Pb. PMT 2003 MCQ

A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is

A

250 N

B

750 N

C

1000 N

D

1200 N

Question 218: Palette 218/257

Errorless DCE 1999, 2001, 09; Kerala PET 2011 MCQ

A block of mass m at the end of a string is whirled round in a vertical circle of radius R. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is

A

Rg

B

$(Rg)^{2}$

C

R/g

D

$\sqrt{Rg}$

Question 219: Palette 219/257

Errorless CPMT 1999; MH CET 2004 MCQ

The minimum velocity at the lowest point, so that the string just slack at the highest point in a vertical circle of radius l

A

$\sqrt{gl}$

B

$\sqrt{3gl}$

C

$\sqrt{5gl}$

D

$\sqrt{7gl}$

Question 220: Palette 220/257

Errorless KCET 1999; BHU 2003 MCQ

The maximum range of a gun on horizontal terrain is 16 km. If $g = 10m/s^{2}$ . What must be the muzzle velocity of the shell

A

200 m/s

B

400 m/s

C

100 m/s

D

50 m/s

Question 221: Palette 221/257

Errorless BHU 1999; AMU (Engg.) 2000; DPMT 2001 MCQ

A ball is thrown upwards and it returns to ground describing a parabolic path. Which of the following remains constant

A

Kinetic energy of the ball

B

Speed of the ball

C

Horizontal component of velocity

D

Vertical component of velocity

Question 222: Palette 222/257

Errorless AMU (Engg.) 1999; JIPMER 2001, 02 MCQ

The kinetic energy k of a particle moving along a circle of radius R depends on the distance covered s as $k = as^{2}$ where a is a constant. The force acting on the particle is

A

$2a\frac{s^{2}}{R}$

B

$2as\left(1 + \frac{s^{2}}{R^{2}}\right)^{1/2}$

C

2as

D

$2a\frac{R^{2}}{s}$

Question 223: Palette 223/257

Errorless AIIMS 1998; WB-JEE 2008; Odisha JEE 2011 MCQ

A body of mass 5 kg is moving in a circle of radius 1 m with an angular velocity of 2 radian/sec. The centripetal force is

A

10 N

B

20 N

C

30 N

D

40 N

Question 224: Palette 224/257

Errorless AIIMS 1998; CBSE PMT 2000; DPMT 2000; RPET 2001; Kerala PET 2005; KCET 2007 MCQ

The horizontal range is four times the maximum height attained by a projectile. The angle of projection is

A

$90^{\circ}$

B

$60^{\circ}$

C

$45^{\circ}$

D

$30^{\circ}$

Question 225: Palette 225/257

Errorless MP PET 1997; AFMC 2006 MCQ

A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it

A

Increases

B

Decreases

C

Remains the same

D

Fluctuates

Question 226: Palette 226/257

Errorless CPMT 1997; RPMT 1999, 2006; BHU 2000; MH CET 2000, 01; MH CET 2002; CPMT 2003 MCQ

The angular speed of seconds needle in a mechanical watch is

A

$\frac{\pi}{30}$ rad/s

B

$2\pi$ rad/s

C

$\pi$ rad/s

D

$\frac{60}{\pi}$ rad/s

Question 227: Palette 227/257

Errorless RPET 1997; RPMT 2005 MCQ

A hollow sphere has radius 6.4 m. Minimum velocity required by a motor cyclist at bottom to complete the circle will be

A

17.7 m/s

B

10.2 m/s

C

12.4 m/s

D

16.0 m/s

Question 228: Palette 228/257

Errorless MP PET 1997, 2010; UP CPMT 2006 MCQ

The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5t^2) m$ and $x = 6t m$ , where $t$ is in second. The velocity with which the projectile is projected is

A

$8m/sec$

B

$6m/sec$

C

$10m/sec$

D

Not obtainable from the data

Question 229: Palette 229/257

Errorless CBSE PMT 1997, 2001; AIEEE 2002; Pb. PMT 2004; Odisha PMT 2004; WB-JEE 2009, 12 MCQ

A ball is projected with kinetic energy E at an angle of $45^{\circ}$ to the horizontal. At the highest point during its flight, its kinetic energy will be

A

Zero

B

E/2

C

$E/\sqrt{2}$

D

E

Question 230: Palette 230/257

Errorless CPMT 1997; AIEEE 2003 MCQ

The coordinates of a moving particle at any time 't' are given by $x = \alpha t^{3}$ and $y = \beta t^{3}$ . The speed of the particle at time 't' is given by

A

$\sqrt{\alpha^{2} + \beta^{2}}$

B

$3t\sqrt{\alpha^{2} + \beta^{2}}$

C

$3t^{2}\sqrt{\alpha^{2} + \beta^{2}}$

D

$t^{2}\sqrt{\alpha^{2} + \beta^{2}}$

Question 231: Palette 231/257

Errorless CPMT 1996; Pb. PMT 2001; CBSE PMT 2001; AIEEE 2002; Kerala (Med.) 2002; MH CET 2004; Kerala PET 2007 MCQ

A car of mass 800 kg moves on a circular track of radius 40 m. If the coefficient of friction is 0.5, then maximum velocity with which the car can move is

A

7 m/s

B

14 m/s

C

8 m/s

D

12 m/s

Question 232: Palette 232/257

Errorless RPET 1996; MH CET 2002; MP PMT 2003; Kerala PET 2009 MCQ

A car is moving with speed 30 m/sec on a circular path of radius 500 m. Its speed is increasing at the rate of $2m/sec^{2}$ , What is the acceleration of the car

A

$2m/sec^{2}$

B

$2.7m/sec^{2}$

C

$1.8m/sec^{2}$

D

$9.8m/sec^{2}$

Question 233: Palette 233/257

Errorless CPMT 1996; RPMT 2000; AFMC 2001; JIPMER 2001, 02 MCQ

An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

A

1200 m

B

0.33 km

C

3.33 km

D

33 km

Question 234: Palette 234/257

Errorless Kurukshetra CEE 1996; Pb. PET 2001; BCECE 2003; RPMT 2006; Odisha JEE 2011 MCQ

The angle of projection at which the horizontal range and maximum height of projectile are equal is

A

$45^{\circ}$

B

$\theta = \tan^{-1}(0.25)$

C

$\theta = \tan^{-1} 4$ or $(\theta = 76^{\circ})$

D

$60^{\circ}$

Question 235: Palette 235/257

Errorless CBSE PMT 1995; SCRA 1998; Pb. PMT 1999; DPMT 2000; AFMC 2002; CPMT 2002 MCQ

The angular speed of a fly wheel making 120 revolutions/minute is

A

$2\pi$ rad/s

B

$4\pi^2$ rad/s

C

$\pi$ rad/s

D

$4\pi$ rad/s

Question 236: Palette 236/257

Errorless EAMCET (Med.) 1995; AMU (Engg.) 2001; Odisha JEE 2009; Kerala PET 2011 MCQ

If a particle of mass m is moving in a horizontal circle of radius r with a centripetal force $(-k/r^{2})$ , the total energy is

A

$-\frac{k}{2r}$

B

$-\frac{k}{r}$

C

$-\frac{2k}{r}$

D

$-\frac{4k}{r}$

Question 237: Palette 237/257

Errorless RPET 1995; UPSEAT 2002; MH CET 2002; RPMT 2006; MP PET 2010 MCQ

A cane filled with water is revolved in a vertical circle of radius 4 m and the water just does not fall down. The time period of revolution will be

A

1 sec

B

10 sec

C

8 sec

D

4 sec

Question 238: Palette 238/257

Errorless EAMCET (Med.) 1995; MH CET 2003; BCECE 2004 MCQ

A person sitting in an open car moving at constant velocity throws a ball vertically up into air. The ball falls

A

Outside the car

B

In the car ahead of the person

C

In the car to the side of the person

D

Exactly in the hand which threw it up

Question 239: Palette 239/257

Errorless EAMCET (Med.) 1995; Pb. PMT 2000; AIIMS 2001; Odisha JEE 2010 MCQ

Two bodies are projected with the same velocity. If one is projected at an angle of $30^{\circ}$ and the other at an angle of $60^{\circ}$ to the horizontal, the ratio of the maximum heights reached is

A

3:1

B

1:3

C

1:2

D

2:1

Question 240: Palette 240/257

Errorless MCQ

A particle is moving with a uniform speed v in a circular path of radius r with the centre at O. When the particle moves from a point P to Q on the circle such that $\angle POQ = \theta$ , then the magnitude of the change in velocity is

A

$2v \sin(2\theta)$

B

Zero

C

$2v \sin\left(\frac{\theta}{2}\right)$

D

$2v \cos\left(\frac{\theta}{2}\right)$

Question 241: Palette 241/257

Errorless MCQ

An object is tied to a string of length $l$ and is revolved in a vertical circle at the minimum velocity. When the object reaches the uppermost point, the string breaks and it describes a parabolic path as shown in the figure under the gravitational force. The horizontal range $AC$ in the plane of $A$ would be

A

l

B

2l

C

$\sqrt {2} l$

D

$2 \sqrt {2} I$

Question 242: Palette 242/257

Errorless MCQ

A projectile is fired from the surface of the earth with a velocity of $5 \, ms^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3 \, ms^{-1}$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $ms^{-2}$ ) is (given $g = 9.8 \, ms^{-2}$ )

A

16.3

B

110.8

C

3.5

D

5.9

Question 243: Palette 243/257

Errorless MCQ

A block of mass 10kg is in contact against the inner wall of a hollow cylindrical drum of radius 1m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis, will be $(g = 10m/s^{2})$

A

$\sqrt{10}rad/s$

B

$\frac{10}{2\pi}rad/s$

C

10rad/s

D

$10\pi rad/s$

Question 244: Palette 244/257

Errorless MCQ

A balloon is moving up in air vertically above a point $A$ on the ground. When it is at a height $h_1$ , a girl standing at a distance $d$ (point $B$ ) from $A$ (see figure) sees it at an angle $45^\circ$ with respect to the vertical. When the balloon climbs up a further height $h_2$ , it is seen at an angle $60^\circ$ with respect to the vertical if the girl moves further by a distance $2.464 d$ (point $C$ ). Then the height $h_2$ is (given $\tan 30^\circ = 0.5774$ )

A

d

B

0.732 d

C

1.464 d

D

0.464 d

Question 245: Palette 245/257

Errorless MCQ

Assertion : In projectile motion, the angle between the instantaneous velocity and acceleration at the highest point is $180^{\circ}$ . Reason : At the highest point, velocity of projectile will be in horizontal direction only.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 246: Palette 246/257

Errorless MCQ

Assertion : Two particles of different mass, projected with same velocity at same angles. The maximum height attained by both the particle will be same. Reason : The maximum height of projectile is independent of particle mass.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 247: Palette 247/257

Errorless MCQ

Assertion : The maximum horizontal range of projectile is proportional to square of velocity. Reason : The maximum horizontal range of projectile is equal to maximum height attained by projectile.

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

E

If assertion is false but reason is true.

Question 248: Palette 248/257

Errorless MCQ

Roads are banked on curves so that

A

The speeding vehicles may not fall outwards

B

The frictional force between the road and vehicle may be decreased

C

The wear and tear of tyres may be avoided

D

The weight of the vehicle may be decreased

Question 249: Palette 249/257

Errorless MCQ

A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is ( $\angle POQ = 40^{\circ}$ )

A

$$<br /> 2 \nu \cos 4 0 ^ {\circ}<br /> $$

B

$$<br /> 2 v \sin 4 0 ^ {\circ}<br /> $$

C

$$<br /> 2 \upsilon \sin 2 0 ^ {\circ}<br /> $$

D

$$<br /> 2 \nu \cos 2 0 ^ {\circ}<br /> $$

Question 250: Palette 250/257

Errorless MCQ

A particle does uniform circular motion in a horizontal plane. The radius of the circle is 20 cm. The centripetal force acting on the particle is 10 N. It's kinetic energy is

A

0.1 J

B

0.2 J

C

2.0 J

D

1.0 J

Question 251: Palette 251/257

Errorless MCQ

A particle moves with constant angular velocity in circular path of certain radius and is acted upon by a certain centripetal force $F$ . If the angular velocity is doubled, keeping radius the same, the new force will be

A

2F

B

$F^2$

C

4F

D

$F / 2$

Question 252: Palette 252/257

Errorless MCQ

A body of mass m kg is rotating in a vertical circle at the end of a string of length r metre. The difference in the kinetic energy at the top and the bottom of the circle is

A

$\frac{mg}{r}$

B

$\frac{2mg}{r}$

C

2mgr

D

mgr

Question 253: Palette 253/257

Errorless MCQ

A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at the rate of 'a' $m/s^2$ , then the resultant acceleration will be

A

$\sqrt{\left\{\frac{v^{2}}{r^{2}}-a^{2}\right\}}$

B

$\sqrt{\left\{\frac{v^{4}}{r^{2}}+a^{2}\right\}}$

C

$\sqrt{\left\{\frac{v^{4}}{r^{2}}-a^{2}\right\}}$

D

$\sqrt{\left\{\frac{v^{2}}{r^{2}}+a^{2}\right\}}$

Question 254: Palette 254/257

Errorless MCQ

A ball of mass 0.1 kg is suspended by a string. It is displaced through an angle of $60^{\circ}$ and left. When the ball passes through the mean position, the tension in the string is

A

19.6 N

B

1.96 N

C

9.8 N

D

Zero

Question 255: Palette 255/257

Errorless MCQ

An aeroplane moving horizontally at a speed of 200 m/s and at a height of $8.0 \times 10^{3}$ m is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released

A

7.234 km

B

8.081 km

C

8.714 km

D

9.124 km

Question 256: Palette 256/257

Errorless MCQ

A ball of mass m is thrown vertically upwards. Another ball of mass 2m is thrown at an angle $\theta$ with the vertical. Both of them stay in air for same period of time. The heights attained by the two balls are in the ratio of

A

2:1

B

1:cos $\theta$

C

1:1

D

cos $\theta$ :1

Question 257: Palette 257/257

Errorless MCQ

A stone is projected from the ground with velocity 50 m/s at an angle of $30^{\circ}$ . It crosses a wall after 3 sec. How far beyond the wall the stone will strike the ground ( $g = 10 \, m/sec^{2}$ )

A

90.2 m

B

89.6 m

C

86.6 m

D

70.2 m