Question 1: Palette 1/206

Errorless JEE (Main) Jan. 2025 MCQ

A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity $v_{0}$ at the point ‘A’. the string becomes slack when, the bob reaches at the point ‘D’. the ration of the kinetic energy of the bob at the points B and C is ____

A

2

B

1

C

4

D

3

Question 2: Palette 2/206

Errorless JEE (Main) Jan. 2025 MCQ

A ball of mass 100 g is projected with velocity 20 m/s at 60° with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

A

20 J

B

15 J

C

zero

D

5 J

Question 3: Palette 3/206

Errorless JEE (Main) Jan. 2025 MCQ

A ball having kinetic energy KE, is projected at an angle of $60^{\circ}$ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight

A

$\frac{(KE)}{8}$

B

$\frac{(KE)}{4}$

C

$\frac{(KE)}{16}$

D

$\frac{(KE)}{2}$

Question 4: Palette 4/206

Errorless JEE (Main) Jan. 2025 MCQ

Two projectiles are fired with same initial speed from same point on ground at angles of $(45^{\circ}-\alpha)$ and $(45^{\circ}+\alpha)$ , respectively, with the horizontal direction. The ratio of their maximum heights attained is

A

$\frac{1-\tan\alpha}{1+\tan\alpha}$

B

$\frac{1+\sin\alpha}{1-\sin\alpha}$

C

$\frac{1-\sin2\alpha}{1+\sin2\alpha}$

D

$\frac{1+\sin2\alpha}{1-\sin2\alpha}$

Question 5: Palette 5/206

Errorless JEE (Main) Jan. 2024 MCQ

A particle moving in a circle of radius R with uniform speed takes time T to complete one revolution. If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to 4R. The angle of projection $\theta$ is then given by

A

$\sin^{-1}\left[\frac{2gT^{2}}{\pi^{2}R}\right]^{\frac{1}{2}}$

B

$\sin^{-1}\left[\frac{\pi^{2}R}{2gT^{2}}\right]^{\frac{1}{2}}$

C

$\cos^{-1}\left[\frac{2gT^{2}}{\pi^{2}R}\right]^{\frac{1}{2}}$

D

$\cos^{-1}\left[\frac{\pi R}{2gT^{2}}\right]^{\frac{1}{2}}$

Question 6: Palette 6/206

Errorless JEE (Main) Jan. 2024 MCQ

Position of an ant (S in metres) moving in Y-Z plane is given by $S = 2t^{2}\hat{j} + 5\hat{k}$ (where t is in second). The magnitude and direction of velocity of the ant at t = 1s will be

A

16 m/s in y-direction

B

4 m/s in x-direction

C

9 m/s in z-direction

D

4 m/s in y-direction

Question 7: Palette 7/206

Errorless JEE (Main) Jan. 2024 MCQ

A body starts moving from rest with constant acceleration covers displacement $S_{1}$ in first $(p-1)$ seconds and $S_{2}$ in first p seconds. The displacement $S_{1} + S_{2}$ will be made in time

A

$(2p+1)s$

B

$\sqrt{(2p^{2}-2p+1)s}$

C

$(2p-1)s$

D

$(2p^{2}-2p+1)s$

Question 8: Palette 8/206

Errorless JEE (Main) Jan. 2024 MCQ

If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, then in order to have constant centripetal force, their velocities will be in the ratio of

A

$\sqrt{3}:2$

B

$1:\sqrt{3}$

C

$\sqrt{3}:1$

D

$2:\sqrt{3}$

Question 9: Palette 9/206

Errorless JEE (Main) Jan. 2024 MCQ

A ball of mass 0.5 kg is attached to a string of length 50 cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 N. The maximum possible value of angular velocity of the ball in rad/s is

A

1600

B

40

C

1000

D

20

Question 10: Palette 10/206

Errorless JEE (Main) Jan. 2024 MCQ

A stone of mass 900g is tied to a string and moved in a vertical circle of radius 1m making 10 rpm. The tension in the string, when the stone is at the lowest point is (if $\pi^{2}=9.8$ and $g=9.8m/s^{2}$ )

A

97 N

B

9.8 N

C

8.82 N

D

17.8 N

Question 11: Palette 11/206

Errorless JEE (Main) Jan. 2024 MCQ

A train is moving with a speed of 12 m/s on rails which are 1.5 m apart. To negotiate a curve radius 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g = 10 \, m/s^{2}$ )

A

6.0 cm

B

5.4 cm

C

4.8 cm

D

4.2 cm

Question 12: Palette 12/206

Errorless JEE (Main) April 2024 MCQ

The co-ordinates of a particle moving in x-y plane are given by $x = 2 + 4t, y = 3t + 8t^{2}$ . The motion of the particle is

A

Non-uniformly accelerated

B

Uniformly accelerated having motion along a straight line

C

Uniform motion along a straight line

D

Uniformly accelerated having motion along a parabolic path

Question 13: Palette 13/206

Errorless JEE (Main) April 2024 MCQ

The angle of projection for a projectile to have same horizontal range and maximum height is

A

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

B

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

C

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

D

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

Question 14: Palette 14/206

Errorless JEE (Main) April 2024 MCQ

A clock has 75 cm, 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take $\pi = 3.14$ )

A

139.4

B

140.5

C

220.0

D

118.9

Question 15: Palette 15/206

Errorless JEE (Main) April 2024 MCQ

A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is

A

$6km$

B

$\sqrt{8} km$

C

$4km$

D

$8km$

Question 16: Palette 16/206

Errorless JEE (Main) April 2024 MCQ

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9m and completes 120 revolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $m/s^{2}$ )

A

Zero

B

$16\pi^{2}ms^{-2}$

C

$4\pi^{2}ms^{-2}$

D

$57600\pi^{2}ms^{-2}$

Question 17: Palette 17/206

Errorless JEE (Main) Jan. 2023 MCQ

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

A

192 m

B

136 m

C

272 m

D

68 m

Question 18: Palette 18/206

Errorless JEE (Main) Jan. 2023 MCQ

Two objects are projected with same velocity 'u' however at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha + \beta = 90^{\circ}$ , the ratio of horizontal range of the first object to the $2^{nd}$ object will be

A

4:1

B

2:1

C

1:2

D

1:1

Question 19: Palette 19/206

Errorless JEE (Main) Jan. 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 20: Palette 20/206

Errorless JEE (Main) Jan. 2023 MCQ

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at $x = +2m$ , its velocity is $-4\hat{j}m / s$ . The object's velocity ( $v$ ) and acceleration ( $a$ ) at $x = -2m$ will be

A

$v = 4\hat{i}m / s, a = 8\hat{j}m / s^2$

B

$v = 4\hat{j}m / s, a = 8\hat{i}m / s^2$

C

$v = -4\hat{j}m / s, a = 8\hat{i}m / s^2$

D

$v = -4\hat{i}m / s, a = -8\hat{j}m / s^2$

Question 21: Palette 21/206

Errorless JEE (Main) Jan. 2023 MCQ

A ball of mass 200 g rests on a vertical post of height 20 m. A bullet of mass 10 g, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance 30 m and the bullet at a distance of 120 m from the foot of the post. The value of initial velocity of the bullet will be (if $g = 10 \, m/s^{2}$ )

A

120 m/s

B

60 m/s

C

400 m/s

D

360 m/s

Question 22: Palette 22/206

Errorless JEE (Main) Jan. 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 23: Palette 23/206

Errorless JEE (Main) Jan. 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 24: Palette 24/206

Errorless JEE (Main) Jan. 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 25: Palette 25/206

Errorless JEE (Main) April 2023 MCQ

Two projectiles are projected at $30^{\circ}$ and $60^{\circ}$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is

A

$2:\sqrt{3}$

B

$\sqrt{3}:1$

C

1:3

D

$1:\sqrt{3}$

Question 26: Palette 26/206

Errorless JEE (Main) April 2023 MCQ

A projectile is projected at $30^{\circ}$ from horizontal with initial velocity $40ms^{-1}$ . The velocity of the projectile at t=2s from the start will be (Given $g=10m/s^{2}$ )

A

$20\sqrt{3}ms^{-1}$

B

$40\sqrt{3}ms^{-1}$

C

$20ms^{-1}$

D

Zero

Question 27: Palette 27/206

Errorless JEE (Main) April 2023 MCQ

A particle is moving with constant speed in a circular path. When the particle turns by an angle $90^{\circ}$ , the ratio of instantaneous velocity to its average velocity is $\pi: x\sqrt{2}$ . The value of x will be

A

2

B

5

C

1

D

7

Question 28: Palette 28/206

Errorless JEE (Main) April 2023 MCQ

Two projectiles A and B are thrown with initial velocities of 40 m/s and 60 m/s at angles $30^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively is $(g = 10\,m/s^{2})$

A

$\sqrt{3}:2$

B

$2:\sqrt{3}$

C

1:1

D

4:9

Question 29: Palette 29/206

Errorless JEE (Main) April 2023 MCQ

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: When a body is projected at an angle $45^{\circ}$ , it's range is maximum. Reason R: For maximum range, the value of $\sin2\theta$ should be equal to one. In the light of the above statements, choose the correct answer from the options 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 30: Palette 30/206

Errorless JEE (Main) April 2023 MCQ

As shown in the figure, a particle is moving with constant speed $\pi m / s$ . Considering its motion from $A$ to $B$ , the magnitude of the average velocity is

A

$\pi m / s$

B

$\sqrt{3} m / s$

C

$2\sqrt{3} m / s$

D

$1.5\sqrt{3} m / s$

Question 31: Palette 31/206

Errorless JEE (Main) April 2023 MCQ

A child of mass 5 kg is going round a merry-go-round that makes 1 rotation in 3.14 s. The radius of the merry-go-round is 2 m. The centrifugal force on the child will be

A

80 N

B

50 N

C

100 N

D

40 N

Question 32: Palette 32/206

Errorless JEE (Main) April 2023 MCQ

For particle P revolving round the centre O with radius of circular path r and angular velocity $\omega$ , as shown in below figure, the projection of OP on the x-axis at time t is

A

$x(t) = r\cos \left(\omega t + \frac{\pi}{6}\right)$

B

$x(t) = r\cos (\omega t)$

C

$x(t) = r\sin \left(\omega t + \frac{\pi}{6}\right)$

D

$x(t) = r\cos \left(\omega t - \frac{\pi}{6}\omega\right)$

Question 33: Palette 33/206

Errorless JEE (Main) April 2023 MCQ

The trajectory of projectile, projected from the ground is given by $y = x - \frac{x^{2}}{20}$ . Where x and y are measured in meter. The maximum height attained by the projectile will be

A

5 m

B

$10\sqrt{2}$ m

C

200 m

D

10 m

Question 34: Palette 34/206

Errorless JEE (Main) April 2023 MCQ

The range of the projectile projected at an angle of $15^{\circ}$ with horizontal is 50 m. If the projectile is projected with same velocity at an angle of $45^{\circ}$ with horizontal, then its range will be

A

50 m

B

$50\sqrt{2}$ m

C

100 m

D

$100\sqrt{2}$ m

Question 35: Palette 35/206

Errorless JEE (Main) June 2022 MCQ

A projectile is projected with velocity of 25 m/s at an angle $\theta$ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of $\theta$ will be [use $g = 10 \, m/s^{2}$ ]

A

$\frac{1}{2} \sin^{-1} \left( \frac{5t^{2}}{4R} \right)$

B

$\frac{1}{2} \sin^{-1} \left( \frac{4R}{5t^{2}} \right)$

C

$\tan^{-1} \left( \frac{4t^{2}}{5R} \right)$

D

$\cot^{-1} \left( \frac{R}{20t^{2}} \right)$

Question 36: Palette 36/206

Errorless JEE (Main) June 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 37: Palette 37/206

Errorless JEE (Main) June 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 38: Palette 38/206

Errorless JEE (Main) June 2022 MCQ

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R Assertion A : Two identical balls A and B thrown with same velocity ‘u’ at two different angles with horizontal attained the same range R. If A and B reached the maximum height $h_{1}$ and $h_{2}$ respectively, then $R = 4\sqrt{h_{1}h_{2}}$ Reason R : Product of said heights $h_{1}h_{2}=\left(\frac{u^{2}\sin^{2}\theta}{2g}\right)\cdot\left(\frac{u^{2}\cos^{2}\theta}{2g}\right)$ Choose the CORRECT answer

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.

Question 39: Palette 39/206

Errorless JEE (Main) June 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 40: Palette 40/206

Errorless JEE (Main) June 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 41: Palette 41/206

Errorless JEE (Main) June 2022 MCQ

A projectile is launched at an angle ' $\alpha'$ with the horizontal with a velocity $20ms^{-1}$ . After 10 s, its inclination with horizontal is ' $\beta'$ . The value of tan $\beta$ will be ( $g = 10ms^{-2}$ )

A

$\tan\alpha+5\sec\alpha$

B

$\tan\alpha-5\sec\alpha$

C

$2\tan\alpha-5\sec\alpha$

D

$2\tan\alpha+5\sec\alpha$

Question 42: Palette 42/206

Errorless JEE (Main) June 2022 MCQ

Motion of a particle in $x - y$ plane is described by a set of following equations $x = 4\sin \left(\frac{\pi}{2} -\omega t\right)m$ and $y = 4\sin (\omega t)m$ The path of particle will be

A

Circular

B

Helical

C

Parabolic

D

Elliptical

Question 43: Palette 43/206

Errorless JEE (Main) June 2022 MCQ

A girl standing on road holds her umbrella at $45^{\circ}$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2}kmh^{-1}$ , the rain drops hit her head vertically. The speed of rain drops with respect to the moving girls is

A

$30 kmh^{-1}$

B

$\frac{25}{\sqrt{2}} kmh^{-1}$

C

$\frac{30}{\sqrt{2}} kmh^{-1}$

D

$25 kmh^{-1}$

Question 44: Palette 44/206

Errorless JEE (Main) June 2022 MCQ

The distance of the Sun from Earth is $1.5 \times 10^{11} m$ and its angular diameter is (2000) s when observed from the Earth. The diameter of the Sun will be

A

$2.45 \times 10^{10} m$

B

$1.45 \times 10^{10} m$

C

$1.45 \times 10^{9} m$

D

$0.14 \times 10^{9} m$

Question 45: Palette 45/206

Errorless JEE (Main) July 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

42m

B

47m

C

19m

D

40m

Question 46: Palette 46/206

Errorless JEE (Main) July 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 47: Palette 47/206

Errorless JEE (Main) July 2022 MCQ

A ball is projected from the ground with a speed $15ms^{-1}$ 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 48: Palette 48/206

Errorless JEE (Main) July 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 49: Palette 49/206

Errorless JEE (Main) July 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 50: Palette 50/206

Errorless JEE (Main) July 2022 MCQ

A body of mass 10 kg is projected at an angle of $45^{\circ}$ with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time $t = \frac{T}{\sqrt{2}}$ , is ____ [Take $g = 10 m / s^{2}$ ]

A

$100\hat{i} + (100\sqrt{2} - 200)\hat{j}$

B

$100\sqrt{2}\hat{i} + (100 - 200\sqrt{2})\hat{j}$

C

$100\hat{i} + (100 - 200\sqrt{2})\hat{j}$

D

$100\sqrt{2}\hat{i} + (100\sqrt{2} - 200)\hat{j}$

Question 51: Palette 51/206

Errorless JEE (Main) June 2022 MCQ

A ball is released from rest from point $P$ of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point $Q$ is $A$ while angular position of point $Q$ is $\alpha$ with respect to point $P$ . Which of the following graphs represent the correct relation between $A$ and $\alpha$ when ball goes from $Q$ to $R$

A

B

C

D

Question 52: Palette 52/206

Errorless JEE (Main) July 2022 MCQ

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v. Which of the following curve represents the correct relation between the normal reaction on the block by the wall (N) and speed of the block (v)

A

B

C

D

Question 53: Palette 53/206

Errorless JEE (Advanced) 2022 MCQ

Column-I describes four systems, each with two particles A and B in relative motion as shown in figures. Column-II gives possible magnitudes of their relative velocities (in $ms^{-1}$ ) at time $t = \frac{\pi}{3}s$

Column-I

Column-II

(P) $\frac{\sqrt{3}+1}{2}$ (Q) $\frac {(\sqrt {3} - 1)}{\sqrt {2}}\tag{Q}$ (R) $\sqrt{10}$ (S) $\sqrt {2 5 \pi^ {2} + 1}\tag{T}$

(I) A and B are moving on a horizontal circle of radius 1 m with uniform angular speed $\omega = 1\mathrm{rads}^{-1}$ . The initial angular positions of A and B at time $t = 0$ are $\theta = 0$ and $\theta = \frac{\pi}{2}$ , respectively (II) Projectiles A and B are fired (in the same vertical plane) at t=0 and t=0.1s respectively, with the same speed $v=\frac{5\pi}{\sqrt{2}}ms^{-1}$ and at $45^{\circ}$ from the horizontal plane. The initial separation between A and B is large enough so that they do not collide. ( $g=10ms^{-2}$ ) (III) Two harmonic oscillators A and B moving in the x direction according to $x_{A}=x_{0}\sin\frac{t}{t_{0}}$ and $x_{B}=x_{0}\sin\left(\frac{t}{t_{0}}+\frac{\pi}{2}\right)$ respectively, starting from t=0. Take $x_{0}=1m$ , $t_{0}=1s$ $x_{B}=x_{0}\sin\left(\frac{t}{t_{0}}+\frac{\pi}{2}\right)$ $x_{A}=x_{0}\sin\frac{t}{t_{0}}$ (IV) Particle A is rotating in a horizontal circular path of radius 1 m on the xy plane, with constant angular speed $\omega = 1 rad s^{-1}$ . Particle B is moving up at a constant speed $3 m s^{-1}$ in the vertical direction as shown in the figure. (Ignore gravity) Which one of the following options is correct

A

I→R, II→T, III→P, IV→S

B

I→S, II→P, III→Q, IV→R

C

I→S, II→T, III→P, IV→R

D

I→T, II→P, III→R, IV→S

Question 54: Palette 54/206

Errorless JEE (Main) Feb. 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 55: Palette 55/206

Errorless JEE (Main) March 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 56: Palette 56/206

Errorless JEE (Main) March 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 57: Palette 57/206

Errorless JEE (Main) July 2021 MCQ

A butterfly is flying with a velocity $4\sqrt{2}$ m/s in North-East direction. Wind is slowly blowing at 1 m/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 58: Palette 58/206

Errorless JEE (Main) Aug. 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 59: Palette 59/206

Errorless JEE (Main) Aug. 2021 MCQ

A helicopter is flying horizontally with a speed v at an altitude h has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped

A

$\sqrt{\frac{2ghv^{2}+1}{h^{2}}}$

B

$\sqrt{2ghv^{2}+h^{2}}$

C

$\sqrt{\frac{2gh}{v^{2}}+h^{2}}$

D

$\sqrt{\frac{2v^{2}h}{g}+h^{2}}$

Question 60: Palette 60/206

Errorless JEE (Main) Aug. 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 61: Palette 61/206

Errorless JEE (Main) Aug. 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 62: Palette 62/206

Errorless JEE (Main) March 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 63: Palette 63/206

Errorless JEE (Main) Jan. 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 64: Palette 64/206

Errorless JEE (Main) Sep. 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 65: Palette 65/206

Errorless JEE (Main) Sep. 2020 MCQ

A clock has a continuously moving second's hand of 0.1 m 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 66: Palette 66/206

Errorless JEE (Main) Sep. 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 67: Palette 67/206

Errorless JEE (Main) Sep. 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 68: Palette 68/206

Errorless JEE (Advanced) 2020 MSQ

A student skates up a ramp that makes an angle $30^{\circ}$ with the horizontal. He/She starts (as shown in the figure) at the bottom of the ramp with speed $v_{0}$ and wants to turn around over a semicircular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)

A

$v_{0}^{2}-2gh=\frac{1}{2}gR$

B

$v_{0}^{2} - 2gh = \frac{\sqrt{3}}{2} gR$

C

The centripetal force required at points x and z is zero

D

The centripetal force required is maximum at points x and z

Question 69: Palette 69/206

Errorless JEE (Advanced) 2020 MSQ

Starting at time t=0 from the origin with speed $1ms^{-1}$ , a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation $y=\frac{x^{2}}{2}$ . The x and y components of its acceleration are denoted by $a_{x}$ and $a_{y}$ , respectively. Then

A

$a_{x} = 1ms^{-2}$ implies that when the particle is at the origin, $a_{y} = 1ms^{-2}$

B

$a_{x} = 0$ implies $a_{y} = 1$ ms $^{-2}$ at all times

C

At $t = 0$ , the particle's velocity points in the $x$ -direction

D

$a_x = 0$ implies that $t = 1 \, s$ , the angle between the particle's velocity and the $x$ -axis is $45^\circ$

Question 70: Palette 70/206

Errorless JEE (Main) Jan. 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 71: Palette 71/206

Errorless JEE (Main) Jan. 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 72: Palette 72/206

Errorless JEE (Main) Jan. 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 73: Palette 73/206

Errorless JEE (Main) Jan. 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 74: Palette 74/206

Errorless JEE (Main) Jan. 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 75: Palette 75/206

Errorless JEE (Main) April 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

$14cm$

B

$20cm$

C

$18cm$

D

$26cm$

Question 76: Palette 76/206

Errorless JEE (Main) April 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 77: Palette 77/206

Errorless JEE (Main) April 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 78: Palette 78/206

Errorless JEE (Main) April 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

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

B

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

C

$2g / r$

D

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

Question 79: Palette 79/206

Errorless JEE (Main) April 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 80: Palette 80/206

Errorless JEE (Advanced) 2017 MCQ

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\frac{1}{\rho}\frac{d\rho}{dt}\right)$ is constant. The velocity v of any point on the surface of the expanding sphere is proportional to

A

$R^{3}$

B

R

C

$R^{2/3}$

D

$\frac{1}{R}$

Question 81: Palette 81/206

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 82: Palette 82/206

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 $R = 2.5m$ at a given instant of time. The speed of the particle is

A

6.2 m/s

B

4.5 m/s

C

5.0 m/s

D

5.7 m/s

Question 83: Palette 83/206

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 84: Palette 84/206

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 85: Palette 85/206

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 86: Palette 86/206

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 87: Palette 87/206

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 88: Palette 88/206

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 89: Palette 89/206

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 90: Palette 90/206

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 91: Palette 91/206

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 92: Palette 92/206

Errorless JEE (Advanced) 2013 MCQ

A particle of mass m is projected from the ground with an initial speed $u_{0}$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed $u_{0}$ . The angle that the composite system makes with the horizontal immediately after the collision is

A

$\frac{\pi}{4}$

B

$\frac{\pi}{4} + \alpha$

C

$\frac{\pi}{4} - \alpha$

D

$\frac{\pi}{2}$

Question 93: Palette 93/206

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 94: Palette 94/206

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 95: Palette 95/206

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 96: Palette 96/206

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 97: Palette 97/206

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 98: Palette 98/206

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 99: Palette 99/206

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 100: Palette 100/206

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 101: Palette 101/206

Errorless IIT JEE 2012 MCQ

Consider a disc rotating in the horizontal plane with a constant angular speed $\omega$ about its centre $O$ . The disc has a shaded region on one side of the diameter and an unshanded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles $P$ and $Q$ are simultaneously projected at an angle towards $R$ . The velocity of projection is in the $y-z$ plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed $\frac{1}{8}$ rotation. (ii) their range is less than half the disc radius, and (iii) $\omega$ remains constant throughout. Then

A

P lands in the shaded region and Q in the unshaded region

B

$P$ lands in the unshaded region and $Q$ in the shaded region

C

Both $P$ and $Q$ land in the unshaded region

D

Both $P$ and $Q$ land in the shaded region

Question 102: Palette 102/206

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 103: Palette 103/206

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 104: Palette 104/206

Errorless CBSE PMT (Pre.) 2011 MCQ

A particle moves in a circle of radius 5 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 105: Palette 105/206

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 106: Palette 106/206

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 107: Palette 107/206

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 108: Palette 108/206

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 109: Palette 109/206

Errorless DUMET 2010 MCQ

A child travelling in a train throws a ball outside with a speed V. According to a child 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 110: Palette 110/206

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 111: Palette 111/206

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

$-mgv_0t^2\cos \theta \hat{j}$

C

$mgv_0t\cos \theta \hat{k}$

D

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

Question 112: Palette 112/206

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 113: Palette 113/206

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 114: Palette 114/206

Errorless AIEEE 2010; JEE (Main) April 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 115: Palette 115/206

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 116: Palette 116/206

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 117: Palette 117/206

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 118: Palette 118/206

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

$54^{\circ}$

B

$125^{\circ}$

C

$27^{\circ}$

D

$18^{\circ}$

Question 119: Palette 119/206

Errorless DUMET 2009 MCQ

On the centre of a frictionless table a small hole is made, through which a weightless string of length 2l is inserted. On the two ends of the string two balls of the same mass m are attached. Arrangement is made in such a way that half of the string is on the table top and half is hanging below. The ball on the table top is made to move in a circular path with a constant speed v. What is the centripetal acceleration of the moving ball

A

mvl

B

g

C

Zero

D

2mvl

Question 120: Palette 120/206

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 121: Palette 121/206

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 122: Palette 122/206

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 $20m$ . 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 123: Palette 123/206

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 124: Palette 124/206

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 125: Palette 125/206

Errorless MP PET 2008; JEE (Main) Feb. 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 126: Palette 126/206

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 127: Palette 127/206

Errorless Odisha JEE 2008 MCQ

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

A

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

B

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

C

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

D

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

Question 128: Palette 128/206

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 129: Palette 129/206

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 130: Palette 130/206

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 131: Palette 131/206

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 132: Palette 132/206

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 133: Palette 133/206

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 $T$ is the tension in the string

Question 134: Palette 134/206

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 135: Palette 135/206

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 136: Palette 136/206

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 137: Palette 137/206

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 138: Palette 138/206

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 139: Palette 139/206

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 140: Palette 140/206

Errorless CBSE PMT 2006; DCE 2006; JEE (Main) Jan. 2022, 25, July 2022 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 141: Palette 141/206

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 142: Palette 142/206

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 143: Palette 143/206

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 144: Palette 144/206

Errorless J & K CET 2005 MCQ

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

A

$0.25\mathrm{cm}$

B

$2\mathrm{cm}$

C

$4\mathrm{cm}$

D

$2.5\mathrm{cm}$

Question 145: Palette 145/206

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 146: Palette 146/206

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 147: Palette 147/206

Errorless Odisha JEE 2005 MCQ

The angle turned by a body undergoing circular motion depends on time as $\theta = \theta_0 + \theta_1t + \theta_2t^2$ . Then the angular acceleration of the body is

A

$\theta_{1}$

B

$\theta_{2}$

C

$2\theta_{1}$

D

$2\theta_{2}$

Question 148: Palette 148/206

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 149: Palette 149/206

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 150: Palette 150/206

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 151: Palette 151/206

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 152: Palette 152/206

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 153: Palette 153/206

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 154: Palette 154/206

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 155: Palette 155/206

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 156: Palette 156/206

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 157: Palette 157/206

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 158: Palette 158/206

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 159: Palette 159/206

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 160: Palette 160/206

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 161: Palette 161/206

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 162: Palette 162/206

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 163: Palette 163/206

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 164: Palette 164/206

Errorless Pb. PET 2003 MCQ

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

A

$\sqrt{98}$ m/s

B

7 m/s

C

$\sqrt{490}$ m/s

D

$\sqrt{4.9}$

Question 165: Palette 165/206

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 166: Palette 166/206

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 167: Palette 167/206

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 168: Palette 168/206

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 $5\mathrm{m / sec}$ 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 169: Palette 169/206

Errorless BHU 2002; DPMT 2004; JEE (Main) Jan. 2025 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

2 ML

C

4 ML

D

16 ML

Question 170: Palette 170/206

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 171: Palette 171/206

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 172: Palette 172/206

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 173: Palette 173/206

Errorless CBSE 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 174: Palette 174/206

Errorless IIT-JEE (Screening) 2001 MCQ

A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

A

B

C

D

Question 175: Palette 175/206

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 176: Palette 176/206

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 177: Palette 177/206

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 178: Palette 178/206

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 179: Palette 179/206

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 180: Palette 180/206

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 $10\mathrm{cm}$ 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 181: Palette 181/206

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 182: Palette 182/206

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 183: Palette 183/206

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 184: Palette 184/206

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 185: Palette 185/206

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 186: Palette 186/206

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 187: Palette 187/206

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 188: Palette 188/206

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 189: Palette 189/206

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 190: Palette 190/206

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

8 m/sec

B

6 m/sec

C

10 m/sec

D

Not obtainable from the data

Question 191: Palette 191/206

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 192: Palette 192/206

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 193: Palette 193/206

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 194: Palette 194/206

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 195: Palette 195/206

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 196: Palette 196/206

Errorless MNR 1995; CBSE PMT 1999; UPSEAT 2000 MCQ

Two racing 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 each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is

A

$m_{1}:m_{2}$

B

$r_{1}:r_{2}$

C

1:1

D

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

Question 197: Palette 197/206

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

$2\pi \mathrm{rad} / \mathrm{s}$

B

$4\pi^2 \mathrm{rad} / \mathrm{s}$

C

$\pi \mathrm{rad} / \mathrm{s}$

D

$4\pi \mathrm{rad} / \mathrm{s}$

Question 198: Palette 198/206

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 199: Palette 199/206

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 200: Palette 200/206

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 201: Palette 201/206

Errorless 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 202: Palette 202/206

Errorless MCQ

A small roller coaster starts at point A with a speed u on a curved track as shown in the figure The friction between the roller coaster and the track is negligible and it always remains in contact with the track. The speed of roller coaster at point D on the track will be

A

$(u ^ {2} + g h) ^ {\frac {1}{2}}$

B

$(u^{2} + 2gh)^{\frac{1}{2}}$

C

$(u^{2}+4gh)^{\frac{1}{2}}$

D

u

Question 203: Palette 203/206

Errorless MCQ

Statement-1 : During flight under action of gravity, the change in velocity of a projectile in same time intervals is same. (Neglect air friction) Statement-2 : Neglecting air friction, the acceleration of projectile is constant during flight.

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 204: Palette 204/206

Errorless MCQ

The instant of time at which acceleration and velocity are perpendicular is

A

0.6 sec

B

1.2 sec

C

2.4 sec

D

None of these

Question 205: Palette 205/206

Errorless MCQ

The instant of time at which speed of particle is least

A

0.6 sec

B

1.2 sec

C

2.4 sec

D

None of these

Question 206: Palette 206/206

Errorless MCQ

The instant of time t at which acceleration of particle is perpendicular to its displacement (displacement from t=0 till that instant t) is

A

0.6 sec

B

1.2 sec

C

2.4 sec

D

None of these