Question 1: Palette 1/207

Advance Online April 2019 MCQ

A plane is inclined at an angle $30^{\circ}$ with respect to the horizontal. A particle is projected with a speed $2 \, ms^{-1}$ , from the base of the plane, making an angle $15^{\circ}$ 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 $g = 10 \, ms^{-2}$ )

A

$18\mathrm{cm}$

B

$20\mathrm{cm}$

C

$14\mathrm{cm}$

D

$26\mathrm{cm}$

Question 2: Palette 2/207

Advance Online 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 $t_{1}t_{2}$ is

A

$\frac{R}{2g}$

B

$\frac{2R}{g}$

C

$\frac{R}{g}$

D

$\frac{R}{4g}$

Question 3: Palette 3/207

Advance Online 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 $(g = 10 \, \text{ms}^{-2})$

A

$\theta_{0} = \sin^{-1}\left(\frac{1}{\sqrt{5}}\right)$ and $v_{0} = \frac{5}{3} \, ms^{-1}$

B

$\theta_{0} = \cos^{-1}\left(\frac{2}{\sqrt{5}}\right)$ and $v_{0} = \frac{3}{5} \, ms^{-1}$

C

$\theta_{0} = \cos^{-1}\left(\frac{1}{\sqrt{5}}\right)$ and $v_{0} = \frac{5}{3} \, ms^{-1}$

D

$\theta_{0} = \sin^{-1}\left(\frac{2}{\sqrt{5}}\right)$ and $v_{0} = \frac{3}{5} \, ms^{-1}$

Question 4: Palette 4/207

Advance Online 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

$R^{2}=4h_{1}h_{2}$

B

$R^{2}=16h_{1}h_{2}$

C

$R^{2}=2h_{1}h_{2}$

D

$R^{2}=h_{1}h_{2}$

Question 5: Palette 5/207

Advance Online January 2019 MCQ

Two guns A and B can fire bullets at speeds $1 \, kms^{-1}$ and $2 \, kms^{-1}$ 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

1:4

B

1:8

C

1:2

D

1:16

Question 6: Palette 6/207

Advance Online 2015 MCQ

If a body moving in a circular path maintains constant speed of $10\mathrm{ms}^{-1}$ , then which of the following correctly describes relation between acceleration and radius?

A

B

C

D

Question 7: Palette 7/207

Advance 2013 MCQ

A projectile is given an initial velocity of $\left(\hat{i}+2\hat{j}\right)\mathrm{ms}^{-1}$ , where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g=10~ms^{-2}$ , the equation of its trajectory is

A

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

B

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

C

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

D

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

Question 8: Palette 8/207

Advance 2012 MCQ

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

A

10 m

B

$10\sqrt{2}$ m

C

20 m

D

$20\sqrt{2}$ m

Question 9: Palette 9/207

Advance 2011 MCQ

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is

A

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

B

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

C

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

D

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

Question 10: Palette 10/207

Advance 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

A

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

B

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

C

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

D

$-\frac{1}{2} mgv_0t^2\cos \theta \hat{k}$
where $\hat{i}$ , $\hat{j}$ and $\hat{k}$ are unit vectors along x, y and z-axis respectively.

Question 11: Palette 11/207

Advance 2010 MCQ

For a particle in uniform circular motion, the acceleration $\vec{a}$ at a point $P(R,\theta)$ on the circle of radius $R$ is (Here $\theta$ is measured from the $x$ -axis)

A

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

B

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

C

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

D

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

Question 12: Palette 12/207

Advance 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

$14\mathrm{ms}^{-2}$

B

$13\mathrm{ms}^{-2}$

C

$12\mathrm{ms}^{-2}$

D

$7.2\mathrm{ms}^{-2}$

Question 13: Palette 13/207

Advance 2000 MCQ

The rotor of a turbine rotates at the rate of 2000 rpm. If the diameter of the rotor is 5 m, the centripetal acceleration at the edge of the rotor is (take $\pi^{2}=10$ )

A

$11\times10^{5}$ ms $^{-2}$

B

$1.1\times10^{5}$ ms $^{-2}$

C

$2.2\times10^{4}$ ms $^{-2}$

D

$2.2\times10^{5}$ ms $^{-2}$

Question 14: Palette 14/207

Advance 1920 MCQ

A jet plane flying at a constant velocity $v$ at a height $h = 8$ kilometre is being tracked by a radar $R$ located at $O$ directly below the line of flight. If the angle $\theta$ is decreasing at the rate of $0.025 \, \mathrm{rads}^{-1}$ , the velocity of the plane when $\theta = 60^{\circ}$ is

A

$1440\mathrm{kmh}^{-1}$

B

$960\mathrm{kmh}^{-1}$

C

$1920\mathrm{kmh}^{-1}$

D

$480\mathrm{kmh}^{-1}$

Question 15: Palette 15/207

Advance MCQ

Two particles $P$ and $Q$ are moving as shown in the figure. At this moment of time the angular speed of $P$ w.r.t. $Q$ is

A

$5\mathrm{rads}^{-1}$

B

$4\mathrm{rads}^{-1}$

C

$2\mathrm{rads}^{-1}$

D

$1\mathrm{rads}^{-1}$

Question 16: Palette 16/207

Advance MCQ

A particle is ejected from the tube at $A$ with a velocity $v$ at an angle $\theta$ with the vertical $y$ -axis. A strong horizontal wind gives the particle a constant horizontal acceleration $a$ in the $x$ -direction. If the particle strikes the ground at a point directly under its released position and the downward $y$ -acceleration is taken as $g$ then

A

$h = \frac{2v^{2}\sin\theta\cos\theta}{a}$

B

$h = \frac{2v^{2}\sin\theta\cos\theta}{g}$

C

$h = \frac{2v^{2}}{g} \sin \theta \left( \cos \theta + \frac{a}{g} \sin \theta \right)$

D

$h = \frac{2v^{2}}{a} \sin \theta \left( \cos \theta + \frac{g}{a} \sin \theta \right)$

Question 17: Palette 17/207

Advance MCQ

The speed of a projectile when it is at its greatest height is $\sqrt{\frac{2}{5}}$ times its speed at half the maximum height. The angle of projection is

A

$3 0 ^ {\circ}$

B

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

C

$4 5 ^ {\circ}$

D

$6 0 ^ {\circ}$

Question 18: Palette 18/207

Advance MCQ

A boy throws a ball upwards with velocity $v_{0} = 20 \, \mathrm{ms}^{-1}$ . The wind imparts a horizontal acceleration of $4 \, \mathrm{ms}^{-2}$ to the left. The angle $\theta$ at which the ball must be thrown so that the ball returns to the boy's hand is $(g = 10 \, \mathrm{ms}^{-2})$

A

$\tan^{-1}(1.2)$

B

$\tan^{-1}(0.2)$

C

$\cot^{-1}

D

$\cot^{-1}(2.5)$

Question 19: Palette 19/207

Advance MCQ

A particle is moving in a circle of radius R in such a way that at any instant the total acceleration makes an angle of $45^{\circ}$ with radius. Initial speed of particle is $v_{0}$ . The time taken to complete the first revolution is

A

$\frac{R}{v_{0}}$

B

$\frac{2R}{v_{0}}$

C

$\frac{R}{v_{0}}e^{-2\pi}$

D

$\frac{R}{v_{0}}(1-e^{-2\pi})$

Question 20: Palette 20/207

Advance MCQ

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

A

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

B

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

C

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

D

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

Question 21: Palette 21/207

Advance MCQ

Starting from rest, a particle rotates in a circle of radius $R = \sqrt{2}$ m with an angular acceleration $\alpha = \frac{\pi}{4}$ rads $^{-2}$ . The magnitude of average velocity of the particle over the time it rotates quarter circle is

A

$1\mathrm{ms}^{-1}$

B

$1.25\mathrm{ms}^{-1}$

C

$1.5\mathrm{ms}^{-1}$

D

$2\mathrm{ms}^{-1}$

Question 22: Palette 22/207

Advance MCQ

A projectile has a horizontal range $R$ for two different angles. If $h_1$ and $h_2$ are the maximum heights reached, then

A

$R = h_1h_2$

B

$R = \sqrt{h_1h_2}$

C

$R = 4\sqrt{h_1h_2}$

D

$R = 2\sqrt{h_1h_2}$

Question 23: Palette 23/207

Advance MCQ

A hollow vertical cylinder of radius $r$ and height $h$ has a smooth internal surface. A small particle is placed in contact with the inner side of the upper rim, at point $A$ and given a horizontal speed $u$ , tangential to the rim. It leaves the lower rim at point $B$ , vertically below $A$ . If $n$ is an integer then

A

$\frac{u}{2\pi r}\sqrt{\frac{2h}{g}} = n$

B

$\frac{h}{2\pi r} = n$

C

$\frac{2\pi r}{h} = n$

D

$\frac{u}{\sqrt{2gh}} = n$

Question 24: Palette 24/207

Advance MCQ

A ball is projected so as to pass a wall at a distance $a$ from the point of projection at an angle of $45^{\circ}$ and falls at a distance $b$ on the other side of the wall. If $h$ is the height of the wall then

A

$h = a\sqrt{2}$

B

$h = b\sqrt{2}$

C

$h = \frac{\sqrt{2}ab}{a + b}$

D

$h = \frac{ab}{a + b}$

Question 25: Palette 25/207

Advance MCQ

A boy wants to throw a ball from a point $A$ so as to just clear the obstruction at $B$ . The minimum horizontal velocity with which the boy should throw the ball is

A

$23.5\mathrm{ms}^{-1}$

B

$235\mathrm{ms}^{-1}$

C

$47\mathrm{ms}^{-1}$

D

$32.5\mathrm{ms}^{-1}$

Question 26: Palette 26/207

Advance MCQ

A ball is thrown vertically upward with a speed $v$ from a point $h$ metre above the ground. The time taken for the ball to hit the ground is

A

$\left(\frac{v}{g}\right)\left(1+\sqrt{1+\frac{2hg}{v^2}}\right)$

B

$\sqrt{1+\left(\frac{2hg}{v^2}\right)}$

C

$\left(\frac{v}{g}\right)\sqrt{1+\left(\frac{2hg}{v^{2'}}\right)}$

D

$\left(\frac{v}{g}\right)\sqrt{1-\left(\frac{2hg}{v^2}\right)}$

Question 27: Palette 27/207

Advance MCQ

The muzzle velocity for a certain rifle is $600 \, ms^{-1}$ . If the rifle is pointed vertically upward and fired from an automobile moving horizontally at a speed of $72 \, kmh^{-1}$ , the radius of curvature of the path of the bullet at maximum altitude is (neglect friction of the air and take $g = 10 \, ms^{-2}$ )

A

400 m

B

200 m

C

40 m

D

20 m

Question 28: Palette 28/207

Advance MCQ

A particle starts from the origin of co-ordinates at time t = 0 and moves in the xy plane with a constant acceleration $\alpha$ in the y-direction. Its equation of motion is $y = \beta x^{2}$ . Its velocity component in the x-direction is

A

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

B

$\sqrt{\frac{\alpha}{2\beta}}$

C

$\sqrt{\frac{2\alpha}{\beta}}$

D

not constant

Question 29: Palette 29/207

Advance MCQ

The speed of a projectile $u$ reduces by $50\%$ on reaching maximum height. The range on the horizontal plane is

A

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

B

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

C

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

D

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

Question 30: Palette 30/207

Advance MCQ

It is observed that a projectile is at the same height at 3 s and 5 s from the start. The time of flight of the projectile is equal to

A

1 s

B

2 s

C

4 s

D

8 s

Question 31: Palette 31/207

Advance MCQ

A helicopter ascending at the rate of $12 \, ms^{-1}$ drops a food packet from a height of 80 m above the ground. The time the packet takes to reach the ground is

A

2.7 s

B

5.5 s

C

11 s

D

16.5 s

Question 32: Palette 32/207

Advance MCQ

A ball is thrown from the top of a staircase which just touches the ceiling and finally hits the bottom of the steps. The initial speed of the ball is

A

$6.3\mathrm{ms}^{-1}$

B

$7.6\mathrm{ms}^{-1}$

C

$63\mathrm{ms}^{-1}$

D

$76\mathrm{ms}^{-1}$

Question 33: Palette 33/207

Advance MCQ

A stone is projected with a velocity of $10 \, ms^{-1}$ at $60^\circ$ to the horizontal. At any instant, the angles of elevation of the stone from the two extremities of the range are $\alpha$ and $\beta$ . Then $\tan \alpha + \tan \beta$ equals

A

$\frac{1}{\sqrt{3}}$

B

$\frac{1}{3}$

C

3

D

$\sqrt{3}$

Question 34: Palette 34/207

Advance MCQ

A particle is projected from the ground with a speed of $20 \, ms^{-1}$ making an angle of $60^\circ$ with the horizontal. The radius of curvature of the path of the particle, when its velocity makes an angle of $30^\circ$ with horizontal is $(g = 10 \, \text{ms}^{-2})$

A

10.6 m

B

12.8 m

C

15.4 m

D

24.2 m

Question 35: Palette 35/207

Advance MCQ

A particle is projected with a certain velocity at an angle $\alpha$ above the horizontal from the foot of an inclined plane of inclination $30^{\circ}$ . If the particle strikes the plane normally then $\alpha$ is equal to

A

$30^{\circ} + \tan^{-1}\left(\frac{1}{2\sqrt{3}}\right)$

B

$30^{\circ} + \tan^{-1}\left(2\sqrt{3}\right)$

C

$60^{\circ}$

D

$30^{\circ} + \tan^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Question 36: Palette 36/207

Advance MCQ

A particle moves along a parabolic path $y = 9x^{2}$ in such a way that the x component of velocity remains constant and has a value $\frac{1}{3} ms^{-1}$ . The acceleration of the particle is

A

$\frac{1}{3}\hat{j}ms^{-2}$

B

$3\hat{j}ms^{-2}$

C

$\frac{2}{3}\hat{j}ms^{-2}$

D

$2\hat{j}ms^{-2}$

Question 37: Palette 37/207

Advance MCQ

A particle moves along a circle of radius R = 2 m so that its radius vector $\vec{r}$ relative to a point on its circumference rotates with the constant angular velocity $\omega = 2 \, rads^{-1}$ . The linear speed of the particle is

A

$4\mathrm{ms}^{-1}$

B

$2\mathrm{ms}^{-1}$

C

$1\mathrm{ms}^{-1}$

D

$8\mathrm{ms}^{-1}$

Question 38: Palette 38/207

Advance MCQ

For two projectiles launched with same initial velocity, the maximum heights corresponding to equal ranges are 4 m and 16 m. The range has a value

A

4 m

B

8 m

C

16 m

D

32 m

Question 39: Palette 39/207

Advance MCQ

When a particle is moving along a circular path with uniform speed, it has

A

radial velocity and radial acceleration

B

radial velocity and transverse acceleration

C

transverse velocity and radial acceleration

D

transverse velocity and transverse acceleration

Question 40: Palette 40/207

Advance MCQ

A particle moves in the xy plane with constant acceleration a directed along the negative y-axis. The equation of motion of the particle has the form $y = \alpha x - \beta x^{2}$ , where $\alpha$ and $\beta$ are positive constants. The velocity of the particle at the origin of coordinates is

A

$\sqrt{a\left(\frac{\alpha^2 + 1}{2\beta}\right)}$

B

$\sqrt{a\left(\frac{\beta + 1}{2\alpha^2}\right)}$

C

$\sqrt{a\left(\frac{\alpha^2 + 1}{4\beta}\right)}$

D

$\sqrt{a\left(\frac{\beta + 1}{4\alpha^2}\right)}$

Question 41: Palette 41/207

Advance MCQ

A body of mass m thrown horizontally with velocity v from the top of the tower of height h touches the ground at a distance of 250 m from the foot of the tower. A body of mass 2m thrown with a velocity of $\frac{v}{2}$ from the top of the tower of height 4h will touch the ground at a distance of

A

250 m

B

500 m

C

1000 m

D

125 m

Question 42: Palette 42/207

Advance MCQ

Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown here. The velocity of A to the left is $10 \, ms^{-1}$ . The speed of B when angle $\theta = 45^{\circ}$ is

A

$5\mathrm{ms}^{-1}$

B

$5\sqrt{2}\mathrm{ms}^{-1}$

C

$7.5\mathrm{ms}^{-1}$

D

$10\mathrm{ms}^{-1}$

Question 43: Palette 43/207

Advance MCQ

A stone is projected so as to pass two walls of heights $a$ and $b$ at distances $b$ and $a$ respectively from the point of projection. If $\alpha$ is the angle of projection then

A

minimum value of tan $\alpha$ is $\sqrt{3}$ .

B

minimum value of tan $\alpha$ is 3.

C

maximum value of tan $\alpha$ is $\sqrt{3}$ .

D

maximum value of tan $\alpha$ is 3.

Question 44: Palette 44/207

Advance MCQ

Two stones are projected so as to reach the same distance from the point of projection on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the heights attained by them. Then the angles of projection for the stones are

A

$45^{\circ}, 135^{\circ}$

B

$0^{\circ}, 90^{\circ}$

C

$30^{\circ}, 60^{\circ}$

D

$20^{\circ}, 70^{\circ}$

Question 45: Palette 45/207

Advance MCQ

Two particles are projected from a point at the same instant with velocities whose horizontal components and vertical components are $(u_{1}, v_{1})$ and $(u_{2}, v_{2})$ , respectively. The time interval between their passing through the other common point of their path (other than origin) is

A

$\frac{2}{g}\left(\frac{v_1u_1 - v_2u_2}{u_1 + u_2}\right)$

B

$\frac{2}{g}\left(\frac{v_1^2 + v_2^2}{u_1 + u_2}\right)$

C

$\frac{2}{g}\left(\frac{u_1^2 + u_2^2}{v_1 + v_2}\right)$

D

$\frac{2}{g}\left(\frac{v_1u_2 - v_2u_1}{u_1 + u_2}\right)$

Question 46: Palette 46/207

Advance MCQ

A pendulum of length $l = 1 \, \text{m}$ is released from $\theta_0 = 60^\circ$ . The rate of change of speed of the bob at $\theta = 30^\circ$ is $(g = 10 \, \text{ms}^{-2})$

A

$2.5\mathrm{ms}^{-2}$

B

$5\mathrm{ms}^{-2}$

C

$5\sqrt{3}\mathrm{ms}^{-2}$

D

$10\mathrm{ms}^{-2}$

Question 47: Palette 47/207

Advance MCQ

A projectile is thrown in a viscous medium offering resistance equal to one-tenth of acceleration due to gravity. The time of flight of projectile will

A

increase by 1%

B

decrease by 1%

C

increase by 2%

D

decrease by 2%

Question 48: Palette 48/207

Advance MCQ

A particle is projected under gravity with velocity $\sqrt{2ag}$ from a point at a height h above the level plane. The maximum range R on the ground is

A

$\sqrt{(a^2 + 1)h}$

B

$\sqrt{a^2h}$

C

$\sqrt{ah}$

D

$2\sqrt{a(a + h)}$

Question 49: Palette 49/207

Advance MCQ

The position vector of particle, moving in x-y plane, at any time t is $\vec{r}=\left[(2t)\hat{i}+\left(2t^{2}\right)\hat{j}\right]$ m. If $\theta$ be the angle which its velocity vector makes with positive x-axis) then the rate of change of $\theta$ at time t=0.5 s.

A

$6\mathrm{rads}^{-1}$

B

$4\mathrm{rads}^{-1}$

C

$2\mathrm{rads}^{-1}$

D

$1\mathrm{rads}^{-1}$

Question 50: Palette 50/207

Advance MCQ

Two particles are projected simultaneously in the same vertical plane, from the same point, but with different speeds and at different angles with the horizontal. The path followed by one, as seen by the other, is

A

a vertical straight line.

B

a straight line making a constant angle ( $\neq90^{\circ}$ ) with the horizontal.

C

a parabola.

D

a hyperbola.

Question 51: Palette 51/207

Advance MCQ

A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t=0. At this instant of time, the horizontal component of its velocity is v. A bead Q of same mass as P is ejected from A at t=0 along the horizontal string AB, with a speed v. Friction between the bead and the string may be neglected. Let $t_{P}$ and $t_{Q}$ be the respective times taken by P and Q to reach the point B, then

A

$t_{\mathrm{P}} < t_{\mathrm{Q}}$

B

$t_{\mathrm{P}} = t_{\mathrm{Q}}$

C

$t_{\mathrm{P}} > t_{\mathrm{Q}}$

D

$\frac{t_{\mathrm{P}}}{t_{\mathrm{Q}}} = \frac{\text{Length of arc } ACB}{\text{Length of chord } AB}$

Question 52: Palette 52/207

Advance MCQ

For the simple pendulum shown, l = 200 mm, when $\theta = 30^{\circ}$ , $\frac{d\theta}{dt} = -9 \, rads^{-1}$ . The magnitude of the total acceleration of the pendulum for this position is

A

$9.81\mathrm{ms}^{-2}$

B

$5\mathrm{ms}^{-2}$

C

$16.2\mathrm{ms}^{-2}$

D

$17\mathrm{ms}^{-2}$

Question 53: Palette 53/207

Advance MCQ

A bomber flying with a horizontal velocity of $500 \, kmh^{-1}$ at a vertical height of 5 km above the ground wants to hit a train moving with a velocity of $100 \, kmh^{-1}$ in the same direction and in the same vertical plane. The angle $\theta$ between the line of sight of the target and the horizontal at the instant the bomb shell should be released is approximately

A

$55^{\circ}$

B

$57^{\circ}$

C

$72^{\circ}$

D

$27^{\circ}$

Question 54: Palette 54/207

Advance MCQ

Four rods each of length l have been hinged to form a rhombus. Vertex A is fixed to rigid support, vertex C is being moved along the x-axis with a constant velocity v as shown in the figure. The rate at which vertex B is approaching the x-axis at the moment the rhombus is in the form of a square is

A

$\frac{v}{\sqrt{2}}$

B

$\frac{v}{2}$

C

$\frac{v}{3}$

D

$\frac{v}{4}$

Question 55: Palette 55/207

Advance MCQ

The distance r from the origin of a particle moving in x-y plane varies with time as, r=2t and the angle made by the radius vector with positive x-axis is $\theta=4t$ . Here, t is in second, r in metres and $\theta$ in radian. The speed of the particle at t=1s is

A

$12\ ms^{-1}$

B

$10\ ms^{-1}$

C

$8.25\ ms^{-1}$

D

$8\ ms^{-1}$

Question 56: Palette 56/207

Advance MCQ

A car enters a curved road in the form of a quarter of a circle, the path length being 200 metre. Its speed at the entrance is $18\mathrm{kmh}^{-1}$ but when it leaves, it increases to $54\mathrm{kmh}^{-1}$ . If the car is travelling with constant acceleration along the curve, the acceleration when the car leaves the curved road is

A

$0.9\mathrm{ms}^{-2}$

B

$0.45\mathrm{ms}^{-2}$

C

$1.9\mathrm{ms}^{-2}$

D

$3.68\mathrm{ms}^{-2}$

Question 57: Palette 57/207

Advance MCQ

The magnitude of displacement of a particle moving in a circle of radius $a$ with constant angular speed $\omega$ varies with time $t$ as

A

$2a\cos (\omega t)$

B

$2a\sin (\omega t)$

C

$2a\cos \left(\frac{\omega t}{2}\right)$

D

$2a\sin \left(\frac{\omega t}{2}\right)$

Question 58: Palette 58/207

Advance MCQ

Two bodies are thrown simultaneously from the same point. One thrown straight up and the other at an angle $\alpha$ with the horizontal. Both bodies have velocity equal to $v_{0}$ . Neglecting the air drag, the separation between the particles at time $t$ is

A

$2v_{0}t\sqrt{1 - \cos\alpha}$

B

$v_{0}t\sqrt{1 - \cos\alpha}$

C

$2v_{0}t\sin \left(\frac{\pi}{4} -\frac{\alpha}{2}\right)$

D

$2v_{0}t\cos \left(\frac{\pi}{4} -\frac{\alpha}{2}\right)$

Question 59: Palette 59/207

Advance MCQ

A boat is moving directly away from the gun on the shore with speed $v_{1}$ . The gun fires a shell with speed $v_{2}$ at an angle $\alpha$ and hits the boat. The distance of the boat from the gun at the moment it is fired is

A

$\frac{2v_{2}\sin\alpha(v_{1}\cos\alpha-v_{2})}{g}$

B

$\frac{2v_{1}\sin\alpha(v_{1}\cos\alpha-v_{2})}{g}$

C

$\frac{2v_{2}\sin\alpha(v_{2}\cos\alpha-v_{1})}{g}$

D

$\frac{2v_{2}\cos\alpha(v_{1}\sin\alpha-v_{2})}{g}$

Question 60: Palette 60/207

Advance MCQ

A projectile is thrown into space so as to have maximum possible range of 400 m. Taking the point of projection as the origin, the co-ordinate of the point where the velocity of the projectile is minimum is

A

(400, 100)

B

(200, 100)

C

(400, 200)

D

(200, 200)

Question 61: Palette 61/207

Advance MCQ

A number of projectiles each with a fixed muzzle velocity u are fired at different angles lying between $0^{\circ}$ and $90^{\circ}$ as shown. Neglecting air resistance and assuming g to be constant, then the equation of the envelope E of the parabolic trajectories (as shown in figure) is

A

$y = \frac{u^2}{2g} -\frac{gx^2}{2u^2}$

B

$y = \frac{gx^2}{2u^2} +\frac{u^2}{2g}$

C

$y = \frac{2u^2}{gx^2} -\frac{2g}{u^2}$

D

$y = \frac{2u^2}{gx^2} +\frac{2g}{u^2}$

Question 62: Palette 62/207

Advance MCQ

A particle $A$ is projected from the ground with an initial velocity of $10\mathrm{ms}^{-1}$ at an angle of $60^{\circ}$ with horizontal. At the same instant, another particle $B$ is projected horizontally with velocity $5\mathrm{ms}^{-1}$ from height $h$ above $A$ so that both the particles collide at point $C$ on the ground. Taking $g = 10\mathrm{ms}^{-2}$ , then

A

$h = 10\mathrm{m}$

B

$h = 30\mathrm{m}$

C

$h = 15\mathrm{m}$

D

$h = 25\mathrm{m}$

Question 63: Palette 63/207

Advance MCQ

A body is projected with a velocity $u$ at an angle $\alpha$ with the horizontal. It passes over a wall at a distance $x$ from the point of projection. The maximum height of the wall corresponds to

A

$\tan \alpha = \frac{u}{gx}$

B

$\tan \alpha = \frac{u^2}{2gx}$

C

$\tan \alpha = \frac{u^2}{gx}$

D

$\tan \alpha = \frac{u^2}{2g}$

Question 64: Palette 64/207

Advance MCQ

In PROBLEM 50, the maximum height of the wall is

A

$h = \frac{u^{2}}{2g}$

B

$h = \frac{gx^{2}}{2u^{2}}$

C

$h = \frac{u^{2}}{2g} + \frac{gx^{2}}{2u^{2}}$

D

$h = \frac{u^{2}}{2g} - \frac{gx^{2}}{2u^{2}}$

Question 65: Palette 65/207

Advance MCQ

Two bodies are projected simultaneously in the same vertical plane, from the same point with different speeds and at different angles of projection with the horizon. The path followed by one projectile as seen from the other is

A

a horizontal straight line.

B

a parabola.

C

a hyperbola.

D

a straight line inclined at an acute angle with the horizontal.

Question 66: Palette 66/207

Advance MCQ

Two particles are projected from the ground simultaneously with speeds $10 \, ms^{-1}$ and $\frac{10}{\sqrt{3}} \, ms^{-1}$ at angles $30^{\circ}$ and $60^{\circ}$ with the horizontal in the same direction. The maximum distance between them till both of them strike the ground is approximately $(g = 10 \, \text{ms}^{-2})$

A

$10\mathrm{m}$

B

$16\mathrm{m}$

C

$23\mathrm{m}$

D

$30\mathrm{m}$

Question 67: Palette 67/207

Advance MCQ

Two particles are projected simultaneously in the same vertical plane from the same point, with different speeds $u_{1}$ and $u_{2}$ , making angles $\theta_{1}$ and $\theta_{2}$ respectively with the vertical, such that $u_{1}\sin \theta_{1} = u_{2}\sin \theta_{2}$ . The path followed by one, as seen by the other (as long as both are in flight), is

A

a straight line making an angle $|\theta_1 - \theta_2|$ with the horizontal.

B

a parabola.

C

a horizontal straight line.

D

a vertical straight line.

Question 68: Palette 68/207

Advance MCQ

A ball rolls of the top of a stair way with a horizontal velocity $u \, ms^{-1}$ . If the steps are h m high and b m wide, the ball will hit the edge of the nth step, if

A

$n = \frac{2hu}{gb^{2}}$

B

$n = \frac{2hu^{2}}{gb^{2}}$

C

$n = \frac{2hu^{2}}{gb}$

D

$n = \frac{hu^{2}}{gb^{2}}$

Question 69: Palette 69/207

Advance MCQ

The trajectory of a projectile in a vertical plane is $y = ax - bx^2$ , where $a, b$ are constants and $x, y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the particle and the angle of projection from the horizontal are

A

$\frac{b^2}{2a}$ , $\tan^{-1}(2a)$

B

$\frac{a^2}{b}$ , $\tan^{-1}(2a)$

C

$\frac{a^2}{4b}$ , $\tan^{-1}(a)$

D

$\frac{2a^2}{b}$ , $\tan^{-1}(a)$

Question 70: Palette 70/207

Advance MCQ

The velocity of a particle moving in the $x - y$ plane is given by $\frac{dx}{dt} = 8\pi \sin (2\pi t)$ and $\frac{dy}{dt} = 8\pi \cos (2\pi t)$ when $t = 0$ , $x = 8$ and $y = 0$ . The path of the particle is

A

a straight line

B

a circle

C

an ellipse

D

a parabola

Question 71: Palette 71/207

Advance MCQ

A projectile is fired with a velocity $u$ at right angle to the slope which is inclined at an angle $\theta$ with the horizontal. The expression for $R$ is

A

$\frac{2u^2}{g}\tan \theta$

B

$\frac{2u^2}{g}\sec \theta$

C

$\frac{u^2}{g}\tan^2\theta$

D

$\frac{2u^2}{g}\tan \theta \sec \theta$

Question 72: Palette 72/207

Advance MCQ

The horizontal range and maximum height attained by a projectile are $R$ and $H$ , respectively. If a constant horizontal acceleration $a = \frac{g}{2}$ is imparted to the projectile due to wind, then its horizontal range and maximum height will be

A

$(R + H), \frac{H}{2}$

B

$\left(R + \frac{H}{2}\right), H$

C

$(R + 2H), H$

D

$(R + H), H$

Question 73: Palette 73/207

Advance MCQ

A particle moves in space along the path $z = ax^{3} + by^{2}$ in such a way that $\frac{dx}{dt} = c = \frac{dy}{dt}$ , where a, b and c are constants. The acceleration of the particle is

A

$(2ax^{2} + 6by^{2})\hat{k}$

B

$(6ac^{2}x + 2bc^{2})\hat{k}$

C

$(bc^{2}x + 2by)\hat{k}$

D

$(4bc^{2}x + 3ac^{2})\hat{k}$

Question 74: Palette 74/207

Advance MCQ

A stone is thrown from a point at a distance $a$ from a wall of height $b$ . If it just clears the wall then the maximum height $h$ reached by the stone for angle of projection $\alpha$ is

A

$\frac{a^2\tan^2\alpha}{4(a\tan\alpha - b)}$

B

$\frac{a^2\sec^2\alpha}{4(a\sec\alpha - b)}$

C

$\frac{a^2\tan^2\alpha}{4b}$

D

$\frac{a^2\tan^2\alpha}{4(a - b\cot\alpha)}$

Question 75: Palette 75/207

Advance MCQ

An aeroplane flying at a constant speed releases a food-packet for flood victims. As the packet drops away from the aeroplane,

A

it will always be vertically below the aeroplane only if the aeroplane was flying at an angle of $45^{\circ}$ to the horizontal.

B

it will always be vertically below the aeroplane only if the aeroplane was flying horizontally.

C

it will gradually fall behind the aeroplane if the aeroplane was flying horizontally.

D

it will always be vertically below the aeroplane.

Question 76: Palette 76/207

Advance MCQ

Position vector of a particle moving in $x - y$ plane at time $t$ is $\vec{r} = a(1 - \cos (\omega t))\hat{i} +a\sin (\omega t)\hat{j}$ . The path of the particle is

A

an ellipse

B

a circle of radius $a$ and centre at $(0,0)$

C

a circle of radius $a$ and centre at $(a,0)$

D

neither a circle nor an ellipse

Question 77: Palette 77/207

Advance MCQ

Ratio of minimum kinetic energies of two projectiles of same mass is 4:1. The ratio of the maximum height attained by them is also 9:1. The ratio of their ranges would be

A

16:1

B

8:1

C

6:1

D

2:1

Question 78: Palette 78/207

Advance MCQ

A person at the point P aims his rifle at an angle of $20^{\circ}$ with the horizontal so that the bullet fired is to hit an object at A but the bullet hits at point B, a vertical distance $\delta$ below A. If the initial velocity of the bullet is $600 \, ms^{-1}$ and the point P is at a horizontal distance of 1 km from the point A then,

A

$\delta = 1543 \, m$

B

$\delta = 154 \, m$

C

$\delta = 154.3 \, m$

D

$\delta = 15.43 \, m$

Question 79: Palette 79/207

Advance MCQ

A particle moves along the positive branch of the curve $y=\frac{x^{2}}{2}$ with x governed by $x=\frac{1}{2}t^{2}$ , where x and y are measured in metre and t in second. At t=2 s, the velocity of the particle is

A

$2\hat{i}-4\hat{j}$ $ms^{-1}$

B

$2\hat{i}+4\hat{j}$ $ms^{-1}$

C

$4\hat{i}+2\hat{j}$ $ms^{-1}$

D

$4\hat{i}-2\hat{j}$ $ms^{-1}$

Question 80: Palette 80/207

Advance MCQ

A particle moves in the x-y plane according to the equations $x = 4t^{2} + 4t + 5$ and $y = -t^{3} + 12t + 3$ . At t = 1 s, the acceleration of the particle is

A

$5 \, ms^{-2}$

B

$10 \, ms^{-2}$

C

$15 \, ms^{-2}$

D

$20 \, ms^{-2}$

Question 81: Palette 81/207

Advance MCQ

A particle is moving in $x - y$ plane. At certain instant of time, the components of its velocity and acceleration are $v_{x} = 3\mathrm{ms}^{-1}$ , $v_{y} = 4\mathrm{ms}^{-1}$ , $a_{x} = 2\mathrm{ms}^{-2}$ and $a_{y} = 1\mathrm{ms}^{-2}$ . The rate of change of speed at this moment is

A

$\sqrt{5}\mathrm{ms}^{-2}$

B

$\sqrt{10}\mathrm{ms}^{-2}$

C

$2\mathrm{ms}^{-2}$

D

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

Question 82: Palette 82/207

Advance MCQ

A particle is projected at an angle of $60^{\circ}$ above the horizontal with a speed of $10\mathrm{ms}^{-1}$ . After some time the direction of its velocity makes an angle of $30^{\circ}$ above the horizontal. The speed of the particle at this instant is

A

$\frac{5}{\sqrt{3}}\mathrm{ms}^{-1}$

B

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

C

$5\mathrm{ms}^{-1}$

D

$\frac{10}{\sqrt{3}}\mathrm{ms}^{-1}$

Question 83: Palette 83/207

Advance MCQ

A particle is thrown with a speed $u$ at an angle $\theta$ with the vertical. When the particle makes an angle $\phi$ with the vertical, its speed changes to $v$ .

A

$v = u\cos \theta$

B

$v = u\sin \theta \cos \phi$

C

$v = u\left(\frac{\sec \phi}{\sec \theta}\right)$

D

$v = u\left(\frac{\csc \phi}{\csc \theta}\right)$

Question 84: Palette 84/207

Advance MCQ

At a height 0.4 m from the ground, the velocity of a projectile in vector form is $\vec{v} = (6\hat{i} + 2\hat{j}) \, \text{ms}^{-1}$ . The angle of projection with the vertical is $(g = 10 \, \text{ms}^{-2})$

A

$45^{\circ}$

B

$60^{\circ}$

C

$30^{\circ}$

D

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

Question 85: Palette 85/207

Advance MCQ

A car moves round a turn of constant curvature between $A$ and $B$ (curve $AB = 100$ metre) with a steady speed of $72 \, \mathrm{kmh}^{-1}$ . If an accelerometer were mounted in the car, the magnitude of acceleration it would record between $A$ and $B$ is

A

ZERO

B

$3.14\mathrm{ms}^{-2}$

C

$31.4\mathrm{ms}^{-2}$

D

$6.28\mathrm{ms}^{-2}$

Question 86: Palette 86/207

Advance MCQ

After one second the velocity of a projectile makes an angle of $45^{\circ}$ with the horizontal. After another 3 s, it is travelling horizontally. The magnitude of its initial velocity and angle of projection are $(g = 10\mathrm{ms}^{-2})$

A

$50~\mathrm{ms}^{-1}$ , $\tan^{-1}\left(\frac{3}{4}\right)$

B

$25~\mathrm{ms}^{-1}$ , $\tan^{-1}\left(\frac{4}{3}\right)$

C

$50~\mathrm{ms}^{-1}$ , $\tan^{-1}\left(\frac{4}{3}\right)$

D

$25~\mathrm{ms}^{-1}$ , $\tan^{-1}\left(\frac{3}{4}\right)$

Question 87: Palette 87/207

Advance MCQ

The minimum speed with which a particle must be projected from the origin so that it just passes through the point $P(30\ \text{m}, 40\ \text{m})$ , taking $g = 10\ ms^{-2}$ , is

A

$30\mathrm{ms}^{-1}$

B

$40\mathrm{ms}^{-1}$

C

$50\mathrm{ms}^{-1}$

D

$60\mathrm{ms}^{-1}$

Question 88: Palette 88/207

Advance MCQ

Two shots are projected from a gun at the top of a cliff with the same velocity $u$ at angles of projection $\alpha$ and $\beta$ with the horizon respectively. If the shots strike the horizontal ground through the foot of the cliff at the same point and if $h$ is the height of the cliff, then

A

$h = \frac{2u^2}{g} \left( \frac{1 - \tan \alpha}{1 - \tan \beta} \right)$

B

$h = \frac{2u^2}{g} (\tan \alpha - \tan \beta)$

C

$h = \frac{2u^2}{g} (\tan \alpha + \tan \beta)$

D

$h = \frac{2u^2}{g} \cot (\alpha + \beta)$

Question 89: Palette 89/207

Advance MCQ

An object is thrown horizontally from a tower at A and hits the ground 3 second later at B. The line of sight from A to B makes an angle of $30^{\circ}$ with the horizontal. The initial velocity of the object, taking $g = 10 \, ms^{-2}$ is

A

$10\mathrm{ms}^{-1}$

B

$13\mathrm{ms}^{-1}$

C

$26\mathrm{ms}^{-1}$

D

$28.8\mathrm{ms}^{-1}$

Question 90: Palette 90/207

Advance MCQ

A point on the rim of a flywheel has a peripheral speed of $10 \, ms^{-1}$ at an instant when it is decreasing at the rate of $60 \, ms^{-2}$ . If the magnitude of the total acceleration of the point at this instant is $100 \, ms^{-2}$ , the radius of the flywheel is

A

25 metre

B

12.5 metre

C

2.5 metre

D

1.25 metre

Question 91: Palette 91/207

Advance MCQ

Water flows from a horizontal pipe which is fixed at a height of 2 m from the ground. If it falls at a distance of 3 m as shown in figure, the speed of water when it leaves the pipe is

A

$4.7\mathrm{ms}^{-1}$

B

$7.4\mathrm{ms}^{-1}$

C

$14.7\mathrm{ms}^{-1}$

D

$47\mathrm{ms}^{-1}$

Question 92: Palette 92/207

Advance MCQ

A particle is projected from the ground with an initial speed of $u$ at an angle $\theta$ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is

A

$\frac{u}{2}\sqrt{1 + 2\cos^2\theta}$

B

$\frac{u}{2}\sqrt{1 + \cos^2\theta}$

C

$\frac{u}{2}\sqrt{1 + 3\cos^2\theta}$

D

$u\cos \theta$

Question 93: Palette 93/207

Advance MCQ

Shots are fired at the same instant from the top and bottom of a vertical cliff at angle $\alpha$ and $\beta$ and they strike an object simultaneously at the same point. If the horizontal distance of the object from the cliff is $l$ and $h$ be the height of the cliff then

A

$h = l(\cot \beta - \cot \alpha)$

B

$h = l(\cos \beta - \cos \alpha)$

C

$h = l(\tan \beta - \tan \alpha)$

D

$h = l(\sin \beta - \sin \alpha)$

Question 94: Palette 94/207

Advance MCQ

A ball thrown upward at an angle of $30^{\circ}$ to the horizontal lands on the top edge of a building 20 metre away. The top edge is 5 metre above the throwing point. The ball was thrown with a velocity of

A

$20 \, ms^{-1}$

B

$30 \, ms^{-1}$

C

$40 \, ms^{-1}$

D

$60 \, ms^{-1}$

Question 95: Palette 95/207

Advance MCQ

A particle is projected vertically upwards from O with velocity v and a second particle is projected at the same instant from P (at a height h above O) with velocity v at an angle of projection $\theta$ . The time when the distance between them is minimum is

A

$\frac{h}{2v\sin\theta}$

B

$\frac{h}{2v\cos\theta}$

C

$\frac{h}{v}$

D

$\frac{h}{2v}$

Question 96: Palette 96/207

Advance MCQ

A projectile is given an initial velocity of $\hat{i} + 2\hat{j}$ . The cartesian equation of its path is $(g = 10 \, \text{ms}^{-2})$

A

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

B

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

C

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

D

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

Question 97: Palette 97/207

Advance MCQ

A ball is launched with an initial velocity of $20\sqrt{2}$ ms $^{-1}$ making at angle $45^{\circ}$ with horizontal. The angular velocity of the particle at highest point of its journey about point of projection is

A

$0.1\ rads^{-1}$

B

$0.2\ rads^{-1}$

C

$0.3\ rads^{-1}$

D

$0.4\ rads^{-1}$

Question 98: Palette 98/207

Advance MCQ

An object is projected up the incline at the angle shown in figure with an initial velocity of $30 \, ms^{-1}$ . The distance x up the incline at which the object lands is

A

$600\mathrm{m}$

B

$104\mathrm{m}$

C

$60\mathrm{m}$

D

$208\mathrm{m}$

Question 99: Palette 99/207

Advance MCQ

A very broad elevator is going up vertically with a constant acceleration of $2 \, ms^{-2}$ . At the instant when its velocity is $4 \, ms^{-1}$ a ball is projected from the floor of the lift with a speed of $4 \, ms^{-1}$ relative to the floor at an elevation of $30^\circ$ . The time taken by the ball to return the floor is $(g = 10 \, \text{ms}^{-2})$

A

1 s

B

$\frac{1}{2} \, s$

C

$\frac{1}{3} \, s$

D

$\frac{1}{4} \, s$

Question 100: Palette 100/207

Advance MCQ

In PROBLEM 86, range of the ball over the floor of the lift is

A

2 m

B

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

C

$\sqrt{3}$ m

D

$2\sqrt{3}$ m

Question 101: Palette 101/207

Advance MCQ

An aircraft moving with a speed of $1000 \, kmh^{-1}$ is at a height of $6000 \, m$ , just overhead of an anti-aircraft gun. If the muzzle velocity is $540 \, ms^{-1}$ , the firing angle $\theta$ should be

A

$73^{\circ}$

B

$30^{\circ}$

C

$59^{\circ}$

D

$45^{\circ}$

Question 102: Palette 102/207

Advance MCQ

A particle moves in the $x$ - $y$ plane with velocity $v_x = 8t - 2$ and $v_y = 2$ . If it passes through the point (14, 4) m at $t = 2$ s, the equation of the path is

A

$x = y^2 - y + 2$

B

$x = y + 2$

C

$x = y^2 + 2$

D

$x = y^2 + y - 2$

Question 103: Palette 103/207

Advance MCQ

A rod of length $l$ leans by its upper end against a smooth vertical wall, while its other end leans against the floor. The end that leans against the wall moves uniformly downward with velocity $v_{0}$ . Then

A

the other end also moves uniformly

B

the speed of other end goes on decreasing

C

the speed of other end goes on increasing

D

the speed of other end first decreases and then increases

Question 104: Palette 104/207

Advance MCQ

A particle is projected from the ground with an initial velocity of $30 \, ms^{-1}$ at an angle of $60^\circ$ with horizontal. The magnitude of change in velocity in 2 s is $(g = 10 \, \text{ms}^{-2})$

A

$5 \, ms^{-1}$

B

$10 \, ms^{-1}$

C

$20 \, ms^{-1}$

D

$40 \, ms^{-1}$

Question 105: Palette 105/207

Advance MCQ

A boy throws a ball with a velocity u at an angle $\alpha$ with the vertical. At the same instant he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of

A

$u \cos \alpha$

B

$u \sin \alpha$

C

$u \tan \alpha$

D

$\sqrt{u^{2} \tan \alpha}$

Question 106: Palette 106/207

Advance MCQ

A projectile is thrown with an initial velocity of $\left(a\hat{i} + b\hat{j}\right)\mathrm{ms}^{-1}$ . If the range of the projectile is twice the maximum height reached by it, then

A

$a = 2b$

B

$b = a$

C

$b = 2a$

D

$b = 4a$

Question 107: Palette 107/207

Advance MCQ

Time taken by the projectile to reach from $A$ to $B$ is $t$ . Then the distance $AB$ is equal to

A

$\frac{ut}{\sqrt{3}}$

B

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

C

$\sqrt{3} ut$

D

$2ut$

Question 108: Palette 108/207

Advance MCQ

A stone is projected from a horizontal plane. It attains maximum height H and strikes a stationary smooth wall and falls on the ground vertically below the maximum height. Assume the collision to be elastic, the height of the point on the wall where stone will strike is

A

$\frac{H}{2}$

B

$\frac{H}{4}$

C

$\frac{3H}{4}$

D

$\frac{H}{3}$

Question 109: Palette 109/207

Advance MCQ

A circular disc of radius $r = 5 \, \text{m}$ is rotating in horizontal plane about $y$ -axis. $Y$ -axis is vertical axis passing through the centre of disc and $x-z$ is the horizontal plane at ground. The height of disc above ground is $h = 5 \, \text{m}$ . Small particles are ejecting from disc in horizontal direction with speed $12 \, \text{ms}^{-1}$ from the circumference of disc then the distance of these particles from origin when they hits the $x-z$ plane is

A

$12 \, \text{m}$

B

$13 \, \text{m}$

C

$5 \, \text{m}$

D

$6 \, \text{m}$

Question 110: Palette 110/207

Advance MCQ

It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation $\frac{5\pi}{36}$ radians should strike a given target. In actual practice it was found that a hill just prevented in the trajectory. At what angle of elevation should the gun be fired to hit the target.

A

$\frac{5\pi}{36}$ radians

B

$\frac{11\pi}{36}$ radians

C

$\frac{7\pi}{36}$ radians

D

$\frac{13\pi}{36}$ radians

Question 111: Palette 111/207

Advance MCQ

A body is thrown with speed of $30 \, ms^{-1}$ at angle $30^{\circ}$ with horizontal from a perfectly inelastic horizontal floor. The time after which it is moving perpendicular to its initial direction of motion is

A

6 s

B

3 s

C

1.5 s

D

never

Question 112: Palette 112/207

Advance MCQ

A body is thrown from a point with speed $50 \, ms^{-1}$ at an angle $37^{\circ}$ with horizontal. When it has moved a horizontal distance of 80 m then its distance from point of projection is

A

40 m

B

$40\sqrt{2}$ m

C

$40\sqrt{5}$ m

D

None of these

Question 113: Palette 113/207

Advance MCQ

A ball is thrown from ground level so as to just clear a wall 4 meters high at a distance of 4 meters and falls at a distance of 14 meters from the wall, then the magnitude of the velocity of the ball is

A

$\sqrt{281}$ ms $^{-1}$

B

$\sqrt{812}$ ms $^{-1}$

C

$\sqrt{182}$ ms $^{-1}$

D

$\sqrt{128}$ ms $^{-1}$

Question 114: Palette 114/207

Advance MCQ

An object is thrown at an angle $\alpha$ to the horizontal $(0^{\circ} < \alpha < 90^{\circ})$ with a velocity. Then during ascent (ignoring air drag) the acceleration

A

with which the object moves is $\vec{g}$ , at all points.

B

tangential to the path decreases.

C

normal to the path increases, becoming equal to $g$ at the highest point.

D

All of these

Question 115: Palette 115/207

Advance MCQ

A projectile is thrown with a velocity of $20 \, ms^{-1}$ , at an angle of $60^\circ$ with the horizontal. After how much time the velocity vector will make an angle of $45^\circ$ with the horizontal? (Take $g = 10 \, ms^{-2}$ )

A

$\sqrt{3} \, s$

B

$\frac{1}{\sqrt{3}} \, s$

C

$(\sqrt{3} + 1) \, s$

D

$(\sqrt{3} - 1) \, s$

Question 116: Palette 116/207

Advance MCQ

A golfer standing on level ground hits a ball with a velocity of $u = 52 \, ms^{-1}$ at an angle $\theta$ above the horizontal. If $\tan\theta = \frac{5}{12}$ , then the time for which the ball is at least 15 m above the ground (i.e. between A and B) will be (take $g = 10 \, ms^{-2}$ )

A

1 s

B

2 s

C

3 s

D

4 s

Question 117: Palette 117/207

Advance MCQ

Which of the following ideas is helpful in understanding projectile motion?

A

$v_{x}^{2} + v_{y}^{2} = constant$

B

Acceleration is +g when the object is rising and -g when falling

C

In the absence of friction the trajectory will depend on the object's mass as well as its initial velocity and launch angle

D

The horizontal motion is independent of the vertical motion

Question 118: Palette 118/207

Advance MCQ

A ball is projected upwards from the top of the 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 the ball will strike the ground?

A

3 s

B

5 s

C

7 s

D

9 s

Question 119: Palette 119/207

Advance MCQ

The equation of projectile is $y = \sqrt{3}x - \frac{g}{2}x^{2}$ . The angle of projection and initial velocity is

A

$30^{\circ}$ , $4\ ms^{-1}$

B

$60^{\circ}$ , $2\ ms^{-1}$

C

$60^{\circ}$ , $4\ ms^{-1}$

D

$90^{\circ}$ , $4\ ms^{-1}$

Question 120: Palette 120/207

Advance MCQ

A projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80~\mathrm{ms}^{-1}$ . Its time of flight is $T$ . Its velocity at $t = \frac{T}{4}$ has a magnitude of nearly

A

$200~\mathrm{ms}^{-1}$

B

$300~\mathrm{ms}^{-1}$

C

$140~\mathrm{ms}^{-1}$

D

$100~\mathrm{ms}^{-1}$

Question 121: Palette 121/207

Advance MCQ

A particle is projected from a point $A$ with velocity $u\sqrt{2}$ at an angle of $45^{\circ}$ with horizontal as shown in figure. It strikes the plane $BC$ at right angles. The velocity of the particle at the time of collision is:

A

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

B

$\frac{u}{2}$

C

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

D

$u$

Question 122: Palette 122/207

Advance MCQ

Consider a boy on a trolley who throws a ball with speed $20 \, ms^{-1}$ at an angle $37^{\circ}$ with respect to trolley in direction of motion of trolley which moves horizontally with speed $10 \, ms^{-1}$ then what will be maximum distance travelled by ball parallel to road

A

20.2 m

B

12 m

C

31.2 m

D

62.4 m

Question 123: Palette 123/207

Advance MCQ

A projectile is thrown at angle $\beta$ with vertical. It reaches a maximum height $H$ . The time taken to reach highest point of its path is

A

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

B

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

C

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

D

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

Question 124: Palette 124/207

Advance MCQ

A body is projected at angle $45^{\circ}$ to horizontal with velocity $20 \, ms^{-1}$ from ground. If there is an acceleration in horizontal direction of $2 \, ms^{-2}$ , then calculate horizontal range of this particle

A

40 m

B

48 m

C

8 m

D

20 m

Question 125: Palette 125/207

Advance MCQ

A particle is projected with a velocity of $20 \, ms^{-1}$ at an angle of $30^{\circ}$ to an inclined plane of inclination $30^{\circ}$ to the horizontal. The particle hits the inclined plane at an angle $30^{\circ}$ , during its journey. The time of flight is

A

$\frac{20\sin(60^{\circ})}{g}$

B

$\frac{20\sin(60^{\circ})}{g\cos(30^{\circ})}$

C

$\frac{20\sin(30^{\circ})}{g\cos(60^{\circ})}$

D

$\frac{20\sin(30^{\circ})}{g}$

Question 126: Palette 126/207

Advance MCQ

A particle starts flying in the $xy$ -plane with a speed of $2\hat{i} + 5x\hat{j}$ . Initial position of the particle was the origin $(0, 0)$ of the plane. The trajectory of the particle is represented by the equation

A

$y = 1.25x^2$

B

$y = 5x^2$

C

$y = 2.5x^2$

D

$x = 5y^2$

Question 127: Palette 127/207

Advance MCQ

The ceiling of a tunnel is 5 m high. What is the maximum horizontal distance that a ball thrown with a speed of $20 \, ms^{-1}$ , can go without hitting the ceiling of the tunnel? (Take $g = 10 \, ms^{-2}$ )

A

30 m

B

40 m

C

$30\sqrt{2} \, m$

D

$20\sqrt{3} \, m$

Question 128: Palette 128/207

Advance MCQ

In projectile motion, the modulus of rate of change of speed

A

is constant

B

first increases then decreases

C

first decreases then increases

D

None of these

Question 129: Palette 129/207

Advance MCQ

If a stone is to hit at a point which is at a horizontal distance d away and at a height h above the point from where the stone starts, then what is the value of initial speed u if the stone is launched at an angle $\theta$ ?

A

$\frac{g}{\cos\theta}\sqrt{\frac{d}{2(d\tan\theta - h)}}$

B

$\frac{d}{\cos\theta}\sqrt{\frac{g}{2(d\tan\theta - h)}}$

C

$\sqrt{\frac{gd^2}{h\cos^2\theta}}$

D

$\sqrt{\frac{gd^2}{d - h}}$

Question 130: Palette 130/207

Advance MCQ

From an inclined plane two particles are projected with same speed at same angle $\theta$ , one up and other down the plane as shown in figure. Which of the following statement(s) is/are correct?

A

The particles will collide the plane with same speed

B

The times of flight of each particle are same

C

Both particles strikes the plane perpendicularly

D

None of these

Question 131: Palette 131/207

Advance MCQ

A large box is moving on horizontal floor with constant acceleration $a = g$ . A particle is projected inside box with velocity $u$ and angle $\theta$ with horizontal with respect to box frame. For the given $u$ , the value of $\theta$ for which horizontal range inside box will be maximum is

A

$\frac{\pi}{4}$

B

$\frac{\pi}{8}$

C

$\frac{3\pi}{8}$

D

$\frac{\pi}{3}$

Question 132: Palette 132/207

Advance MCQ

An object is projected with a velocity of $20 \, ms^{-1}$ making an angle of $45^{\circ}$ with horizontal. The equation for the trajectory is $h = Ax - Bx^{2}$ where h is height, x is horizontal distance. A and B are constants. The ratio A : B is $(g = 10 \, \text{ms}^{-2})$

A

1 : 5

B

5 : 1

C

1 : 40

D

40 : 1

Question 133: Palette 133/207

Advance MCQ

The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x = 2t + 4t^2$ and $y = 5t$ , where $x$ and $y$ are in metre and $t$ in second. The acceleration of the particle at $t = 5\mathrm{s}$ is

A

$40~\mathrm{ms}^{-2}$

B

$20~\mathrm{ms}^{-2}$

C

$8~\mathrm{ms}^{-2}$

D

ZERO

Question 134: Palette 134/207

Advance MCQ

A particle starts from the origin at t = 0. It moves in a plane with a velocity given by $\vec{v} = v_{0}\hat{i} + (a\omega\cos\omega t)\hat{j}$ . The equation of trajectory of the particle is

A

$y = a \sin(\omega t)$

B

$y = a \cos(\omega t)$

C

$y = a \sin\left(\frac{\omega x}{v_{0}}\right)$

D

$y = a \cos\left(\frac{\omega x}{v_{0}}\right)$

Question 135: Palette 135/207

Advance MCQ

Ratio of minimum kinetic energies of two projectiles of same mass is 4:1. The ratio of the maximum height attained by them is also 4:1. The ratio of their ranges would be

A

16:1

B

4:1

C

8:1

D

2:1

Question 136: Palette 136/207

Advance MCQ

At a height 0.4 m from the ground, the velocity of a projectile is, $\vec{v} = (6\hat{i} + 2\hat{j}) \, \text{ms}^{-1}$ . The angle of projection is $(g = 10 \, \text{ms}^{-2})$

A

$45^{\circ}$

B

$60^{\circ}$

C

$30^{\circ}$

D

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

Question 137: Palette 137/207

Advance MCQ

A person standing on a truck moving with a uniform velocity $14.7 \, ms^{-1}$ on a horizontal road throws a ball in such a way that it returns to him after 4 s. The speed and angle of projection as seen by a man on the road are

A

$19.6 \, ms^{-1}$ , vertical

B

$24.5 \, ms^{-1}$ , vertical

C

$19.6 \, ms^{-1}$ , $53^{\circ}$ with the road

D

$24.5 \, ms^{-1}$ , $53^{\circ}$ with the road

Question 138: Palette 138/207

Advance MCQ

Trajectories of two projectiles are shown in the figure. Let $T_{1}$ and $T_{2}$ be the time periods and $u_{1}$ and $u_{2}$ be their speeds of projection. Then

A

$T_{2} > T_{1}$

B

$T_{1} > T_{2}$

C

$u_{1} > u_{2}$

D

$u_{1} < u_{2}$

Question 139: Palette 139/207

Advance MSQ

A bead is free to slide down a smooth wire tightly stretched between the points $P_{1}$ and $P_{2}$ on a vertical circle of radius R. If the bead starts from rest from $P_{1}$ , the highest point on the circle and $P_{2}$ lies anywhere on the circumference of the circle. Then,

A

time taken by bead to go from $P_{1}$ to $P_{2}$ is dependent on position of $P_{2}$ and equals $2\sqrt{\frac{R}{g}}\cos \theta$ .

B

time taken by bead to go from $P_{1}$ to $P_{2}$ is independent of position of $P_{2}$ and equals $2\sqrt{\frac{R}{g}}$ .

C

acceleration of bead along the wire is $g \cos \theta$ .

D

velocity of bead when it arrives at $P_{2}$ is $2\sqrt{gR}\cos\theta$ .

Question 140: Palette 140/207

Advance MSQ

For an oblique projectile, if $T$ is the total time of flight, $H$ the maximum height and $R$ is the horizontal range, then $x$ and $y$ co-ordinates at any time $t$ are related as (neglect air drag)

A

$y = 4H\left(\frac{t}{T}\right)\left(1 - \frac{t}{T}\right)$

B

$y = 4H\left(\frac{T}{t}\right)\left(1 - \frac{T}{t}\right)$

C

$y = 4H\left(\frac{x}{R}\right)\left(1 - \frac{x}{R}\right)$

D

$y = 4H\left(\frac{R}{x}\right)\left(1 - \frac{R}{x}\right)$

Question 141: Palette 141/207

Advance MSQ

From a point P, a particle is projected with a velocity u at an angle $\theta$ with horizontal. At a certain point Q, the particle moves at right angles to its initial direction of motion. Then

A

velocity of particle at Q is $u \sin \theta$ .

B

time of flight from $P$ to $Q$ is $\left(\frac{u}{g}\right)\sec \theta$

C

speed of particle at Q is $u \cot \theta$ .

D

time of flight from $P$ to $Q$ is $\left(\frac{u}{g}\right)\mathrm{cosec}\theta$

Question 142: Palette 142/207

Advance MSQ

A particle is projected with a velocity $2\sqrt{hg}$ so that it just clears two walls of equal height $h$ at horizontal separation $2h$ from each other. Then the

A

angle of projection is $30^{\circ}$ with vertical.

B

angle of projection is $30^{\circ}$ with horizon.

C

time of passing between the walls is $\sqrt{\frac{2h}{g}}$ .

D

time of passing between the walls is $2\sqrt{\frac{h}{g}}$ .

Question 143: Palette 143/207

Advance MSQ

A particle is launched from the origin with an initial velocity $\vec{u} = (3\hat{i})\mathrm{ms}^{-1}$ under the influence of a constant acceleration $\vec{a} = -\left(\hat{i} +\frac{1}{2}\hat{j}\right)\mathrm{ms}^{-2}$ . Its velocity $\vec{v}$ and position vector $\vec{r}$ when it reaches its maximum $x$ -co-ordinate are

A

$\vec{v} = (-1.5\hat{j})\mathrm{ms}^{-1}$

B

$\vec{v} = -2\hat{j}$

C

$\vec{r} = (3\hat{i} -2\hat{j})\mathrm{m}$

D

$\vec{r} = (4.5\hat{i} -2.25\hat{j})\mathrm{m}$

Question 144: Palette 144/207

Advance MSQ

A projectile is projected from the ground making an angle $\alpha$ with the horizontal. Air exerts a drag which is proportional to the velocity of the projectile

A

the time of ascent will be equal to the time of descent

B

the time of ascent will be greater than time of descent

C

the time of descent will be greater than time of ascent

D

at highest point velocity will be horizontal

Question 145: Palette 145/207

Advance MSQ

Two particles projected from the same point with same speed $u$ at angles of projection $\alpha$ and $\beta$ strike the horizontal ground at the same point. If $h_1$ and $h_2$ are the maximum heights attained by projectiles, $R$ be the range for both and $t_1$ and $t_2$ be their time of flights respectively then

A

$\alpha + \beta = \frac{\pi}{2}$

B

$R = 4\sqrt{h_1h_2}$

C

$\frac{t_1}{t_2} = \tan \alpha$

D

$\tan \alpha = \sqrt{\frac{h_1}{h_2}}$

Question 146: Palette 146/207

Advance MSQ

The co-ordinates of a particle moving in a plane are given by $x = a \cos(pt)$ and $y = b \sin(pt)$ , where a, $b (< a)$ and p are positive constants of appropriate dimensions. Then

A

the path of the particle is an ellipse.

B

the velocity and acceleration of the particle are normal to each other at $t=\frac{\pi}{2p}$ .

C

the acceleration of the particle is always directed towards the focus.

D

the distance travelled by the particle in time interval t=0 to $t=\frac{\pi}{2p}$ is a.

Question 147: Palette 147/207

Advance MSQ

A ball starts falling freely from a height h from a point on the inclined plane forming an angle $\alpha$ with the horizontal as shown. After collision with the incline it rebounds elastically off the inclined plane. Then

A

it again strikes the incline at $t=\sqrt{\frac{8h}{g}}$ after it strikes the incline at A.

B

it again strikes the incline at $t=\sqrt{\frac{2h}{g}}$ after it strikes the incline at A.

C

it again strikes the incline at a distance $4h\sin\alpha$ from A along the incline.

D

it again strikes the incline at a distance $8h\sin\alpha$ from A along the incline.

Question 148: Palette 148/207

Advance MSQ

A cart is moving along +x direction with a velocity of $4 \, ms^{-1}$ . A person on the cart throws a stone with a velocity of $6 \, ms^{-1}$ with respect to himself. In the frame of reference of the cart the stone is thrown in the y-z plane making an angle of $30^\circ$ with the vertical z-axis. Then with respect to an observer on the ground

A

the initial velocity of the stone is $10 \, ms^{-1}$

B

the initial velocity of the stone is $2\sqrt{13}$ ms $^{-1}$ .

C

the velocity at the highest point of its motion is zero.

D

the velocity at the highest point of its motion is $5 \, ms^{-1}$ .

Question 149: Palette 149/207

Advance MSQ

Two shells are fired from a cannon successively with speed u each at angles of projection $\alpha$ and $\beta$ , respectively. If the time interval between the firing of shells is t and they collide in mid air after a time T from the firing of the first shell. Then

A

$T \cos \alpha = (T - t) \cos \beta$

B

$\alpha >\beta$

C

$(T-t)\cos\alpha=t\cos\beta$

D

$(u\sin\alpha)T-\frac{1}{2}gT^{2}=(u\sin\beta)(T-t)-\frac{1}{2}g(T-t)^{2}$

Question 150: Palette 150/207

Advance MSQ

Choose the correct alternative (s)

A

A ball is thrown vertically up and another ball is thrown at an angle $\theta$ with the vertical such that both of them remain in air for the same period of time, then the ratio of heights attained by the two balls is 1:1

B

The time of flight T and the horizontal range R of a projectile are connected by the equation $gT^{2}=2R\tan\theta$ , where $\theta$ is the angle of projection

C

For a projectile whose range $R$ is $n$ times its maximum height $H$ the angle of projection is $\tan^{-1}\left(\frac{4}{n}\right)$

D

If the greatest height to which a man can throw a stone is h, then the greatest horizontal distance upto which he can throw the stone is 2h

Question 151: Palette 151/207

Advance MSQ

A radar observer on the ground is watching an approaching projectile. At a certain instant he has the following information. (i) The projectile has reached the maximum altitude and is moving with a horizontal velocity v; (ii) The straight line distance of the observer to the projectile is $l$ ; (iii) The line of sight to the projectile is at an angle $\theta$ above the horizontal. Assuming earth to be flat and the observer lying in the plane of the projectile's trajectory then,

A

the distance between the observer and the point of impact of the projectile is $D = \frac{v^2\sin\theta}{g} - l\cos \theta$ .

B

the distance between the observer and the point of impact of the projectile is $D = v\sqrt{\frac{2l\sin\theta}{g}} - l\cos \theta$ .

C

the projectile will pass over the observer's head for $l < \frac{2v^2\tan\theta\sec\theta}{g}$ .

D

the projectile will pass over the observer's head for $l > \frac{2v^{2} \tan \theta \sec \theta}{g}$ .

Question 152: Palette 152/207

Advance MSQ

A projectile has the same range R for two angles of projections. If $T_{1}$ and $T_{2}$ be the times of flight in the two cases and $\theta$ be the angle of projection corresponding to the time $T_{1}$ , then

A

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

B

$\frac{T_1}{T_2} = \cot \theta$

C

$\frac{T_{1}}{T_{2}}=\tan\theta$

D

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

Question 153: Palette 153/207

Advance MSQ

Two guns situated at the top of a hill of height 10 m, fire one shot each with the same speed of $5\sqrt{3}$ ms $^{-1}$ at some interval of time. One gun fires horizontally and other fires upwards at an angle of 60° with the horizontal. The shots collide in mid air at the point P. Taking the origin of the coordinate system at the foot of the hill right below the muzzle, trajectories in x-y plane and $g = 10 \, ms^{-2}$ , then

A

the first shell reaches the point P at $t_{1}=1$ s from the start.

B

the second shell reaches the point P at $t_{2}=2$ s from the start.

C

the first shell is fired 1 s after the firing of the second shell.

D

they collide at $P$ whose coordinates are given by $(5\sqrt{3}, 5)\mathrm{m}$ .

Question 154: Palette 154/207

Advance MSQ

A projectile is thrown with an initial velocity $u$ , at an angle of projection $\theta$ first from the equator and then from the pole. The fractional decrement in the range of projectile is

A

$\frac{dR}{R} = -\frac{1}{291}$

B

$\frac{dR}{R} = \frac{1}{291}$

C

$\frac{dR}{R} = g\left(\frac{1}{g_p} - \frac{1}{g_e}\right)$

D

$\frac{dR}{R} = -g\left(\frac{1}{g_p} - \frac{1}{g_e}\right)$

Question 155: Palette 155/207

Advance MSQ

A boat is moving directly away from a cannon on the shore with a speed $v_{1}$ . The cannon fires a shell with a speed $v_{2}$ at an angle $\alpha$ and the shell hits the boat. Then,

A

the shell hits the boat when the time equal to $\frac{2v_{2}\sin\alpha}{g}$ is lapsed.

B

the boat travels a distance $\frac{2v_1v_2\sin\alpha}{g}$ from its original position.

C

the distance of the boat from the cannon at the instant the shell is fired is $\frac{2}{g} (v_2\sin \alpha)(v_2\cos \alpha - v_1)$ .

D

the distance of the boat from the cannon when the shell hits the boat is $\frac{2}{g} (v_2\sin \alpha)(v_2\cos \alpha)$ .

Question 156: Palette 156/207

Advance MSQ

A particle is projected from the ground with a velocity $40\sqrt{2}$ ms $^{-1}$ which makes an angle of $45^{\circ}$ with the horizontal. At time t = 2 s

A

displacement of particle is 100 m

B

vertical component of velocity is $20 \, ms^{-1}$

C

velocity makes an angle of $\tan^{-1}

D

particle is at height of 60 m from ground

Question 157: Palette 157/207

Advance MSQ

A particle P lying on smooth horizontal x-y plane starts from $(6\hat{i}+8\hat{j})$ m with velocity $(2\hat{i})$ ms $^{-1}$ . Another particle Q is projected (horizontally from origin with velocity $(a\hat{i}+b\hat{j})$ so that is strikes P after 2 s. Then

A

a=2

B

a=5

C

b=4

D

b=8

Question 158: Palette 158/207

Advance MSQ

A projectile is fired upward with velocity $v_{0}$ at an angle $\theta$ and strikes a point $P(x, y)$ on the roof of the building (as shown). Then,

A

the projectile hits the roof in minimum time if $\theta +\alpha = \frac{\pi}{2}$

B

the projectile hits the roof in minimum time if $\theta +\alpha = \frac{\pi}{4}$

C

the minimum time taken by the projectile to hit the roof is $t_{\min} = \frac{v_{0} - \sqrt{v_{0}^{2} - 2gh\cos^{2}\alpha}}{g\cos\alpha}$ .

D

the projectile never reaches the roof for $v_{0} < \sqrt{2gh}\cos \alpha$ .

Question 159: Palette 159/207

Advance MSQ

A particle is fired from a point on the ground with speed $u$ making an angle $\theta$ with the horizontal. Then

A

the radius of curvature of the projectile at the highest point is $\frac{u^2\cos^2\theta}{g}$

B

the radius of curvature of the projectile at the highest point of launch is $\frac{u^2}{g\cos\theta}$

C

at the point of projection tangential acceleration is $g \sin \theta$

D

at the highest point tangential acceleration is zero

Question 160: Palette 160/207

Advance MSQ

A shot is fired with a velocity u at an angle $(\alpha + \theta)$ with the horizon from the foot of an incline plane of angle $\alpha$ through the point of projection. If it hits the plane horizontally then

A

$\tan\theta=\frac{\tan\alpha}{1+2\tan^{2}\alpha}$

B

$\tan\theta=2\tan\alpha$

C

$\tan\theta=\frac{2\tan\alpha}{1+2\tan^{2}\alpha}$

D

$\tan\theta=\frac{\sin\alpha\cos\alpha}{1+\sin^{2}\alpha}$

Question 161: Palette 161/207

Advance MSQ

Two second after projection, a projectile is travelling in a direction inclined at $30^{\circ}$ to the horizon. After one more second it is travelling horizontally. Then

A

the velocity of projection is $20\mathrm{ms}^{-1}$ .

B

the velocity of projection is $20\sqrt{3}\mathrm{ms}^{-1}$ .

C

the angle of projection is $30^{\circ}$ with vertical.

D

the angle of projection is $30^{\circ}$ with horizon.

Question 162: Palette 162/207

Advance MSQ

A particle is projected from point $A$ with speed $u$ and angle of projection is $60^{\circ}$ . At some instant, magnitude of velocity of particle is $v$ and it makes an angle $\theta$ with horizontal. If radius of curvature of path of particle at the given instant is $\frac{8}{3\sqrt{3}}$ times minimum radius of curvature during the whole flight, then

A

$\theta = 37^{\circ}$

B

$\theta = 30^{\circ}$

C

$v = \frac{u}{\sqrt{3}}$

D

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

Question 163: Palette 163/207

Advance MSQ

Path of a particle moving in $x - y$ plane is $y = 3x + 4$ . At some instant suppose $x$ -component of velocity is $1\mathrm{ms}^{-1}$ and it is increasing at a rate of $1\mathrm{ms}^{-2}$ . Then at this instant

A

speed of particle is $\sqrt{10}\mathrm{ms}^{-1}$

B

acceleration of particle is $\sqrt{10}\mathrm{ms}^{-2}$

C

velocity-time graph is a straight line

D

acceleration-time graph is a straight line

Question 164: Palette 164/207

Advance MSQ

The co-ordinate of the particle in $x - y$ plane are given as $x = 2 + 2t + 4t^2$ and $y = 4t + 8t^2$ . The motion of the particle is

A

along a straight line

B

uniformly accelerated

C

along a parabolic path

D

non-uniformly accelerated

Question 165: Palette 165/207

Advance MSQ

Velocity of a particle moving in a curvilinear path varies with time as $\bar{v} = (2\hat{t}\hat{i} + t^2\hat{j})\mathrm{ms}^{-1}$ , where, $t$ is in second. At $t = 1\mathrm{s}$ , the

A

acceleration of particle is $8\mathrm{ms}^{-2}$ .

B

tangential acceleration of particle is $\frac{6}{\sqrt{5}}\mathrm{ms}^{-2}$ .

C

radial acceleration of particle is $\frac{2}{\sqrt{5}}\mathrm{ms}^{-2}$ .

D

None of these

Question 166: Palette 166/207

Advance MCQ

Statement-1: For an oblique projectile launched from the ground at an angle $\theta$ with the horizontal, $R = H$ at $\theta = \tan^{-1}(4)$ . Statement-2: Maximum range of projectile is proportional to square of initial velocity and inversely proportional to $g$ .

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 167: Palette 167/207

Advance MCQ

Statement-1: The net acceleration of a particle in circular motion is always directed radially inwards. Statement-2: Whenever a particle moves in a circular path, an acceleration exists which is directed towards the centre.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 168: Palette 168/207

Advance MCQ

Statement-1: In uniform circular motion, acceleration is constant. Statement-2: In uniform circular motion, speed is constant.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 169: Palette 169/207

Advance MCQ

Statement-1: When a particle is thrown obliquely from the surface of the Earth, it always moves in a parabolic path, provided the air resistance is negligible. Statement-2: A projectile motion is a two-dimensional motion.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 170: Palette 170/207

Advance MCQ

Statement-1: In uniform circular motion acceleration is constant. Statement-2: In uniform circular motion magnitude of acceleration is $\frac{v^{2}}{r}$ and direction is always towards the centre.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 171: Palette 171/207

Advance MCQ

Statement-1: A particle is moving on a horizontal surface. Its path will be straight line if initial velocity and acceleration are collinear and/or either of them is zero. Statement-2: Angle between $\vec{u}$ and $\vec{a}$ determine path therefore, it may be accelerated or retarded curvilinear.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 172: Palette 172/207

Advance MCQ

Statement-1: When a particle moves in a circle with a uniform speed, its velocity and acceleration both changes. Statement-2: The centripetal acceleration in circular motion is dependent on angular velocity of the body.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 173: Palette 173/207

Advance MCQ

Statement-1: A coin is allowed to fall in a train moving with constant velocity. Its trajectory is parabola as seen by an observer sitting in the train. Statement-2: An observer on ground will see the path of coin as a parabola.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 174: Palette 174/207

Advance MCQ

Statement-1: A particle is projected with a velocity u making at an angle $\theta < 90^{\circ}$ with the horizontal. When particle strikes the ground its speed is again u. Statement-2: Velocity along horizontal direction remains same but velocity along vertical direction is changed. When particle strikes the ground, magnitude of final vertical velocity is equal to magnitude of initial vertical velocity.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 175: Palette 175/207

Advance MCQ

Statement-1: Two particles of different mass, projected with same velocity at same angles. The maximum height attained by both the particles will be same. Statement-2: The maximum height of projectile is independent of the mass of the particle.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 176: Palette 176/207

Advance MCQ

Statement-1: When speed of projection of a body is made n-times, its time of flight becomes n times Statement-2: This is because range of projectile become n times.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 177: Palette 177/207

Advance MCQ

Statement-1: Horizontal velocity of a particle moving under the influence of gravity remains constant. Statement-2: Acceleration due to gravity acts vertically downwards.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 178: Palette 178/207

Advance MCQ

Statement-1: An oblique projectile is launched from the ground to attain a maximum range. The maximum height attained by the projectile is 25% of range. Statement-2: $R = \frac{u^{2} \sin(2\theta)}{g}$ and $H = \frac{u^{2} \sin^{2} \theta}{2g}$

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 179: Palette 179/207

Advance MCQ

Comprehension Passage: Comprehension - 1

A point moves in the plane x, y according to the law $x = kt$ , $y = kt(1 - \alpha t)$ , where k and $\alpha$ are positive constants and t is the time. Based on the above facts, answer the following questions. The trajectory $y(x)$ followed by the particle is a/an

A

straight line

B

ellipse

C

parabola

D

cycloid

Question 180: Palette 180/207

Advance MCQ

Comprehension Passage: Comprehension - 1

A point moves in the plane x, y according to the law $x = kt$ , $y = kt(1 - \alpha t)$ , where k and $\alpha$ are positive constants and t is the time. Based on the above facts, answer the following questions. The velocity $v$ of the point is minimum at time

A

$t = \frac{1}{\alpha}$

B

$t = \frac{1}{2\alpha}$

C

$t = \frac{2}{\alpha}$

D

$t = \frac{1}{3\alpha}$

Question 181: Palette 181/207

Advance MCQ

Comprehension Passage: Comprehension - 1

A point moves in the plane x, y according to the law $x = kt$ , $y = kt(1 - \alpha t)$ , where k and $\alpha$ are positive constants and t is the time. Based on the above facts, answer the following questions. The acceleration of the particle at time when the velocity has a minimum value is

A

$(2 k \alpha) \hat {j}$

B

$(k \alpha) \hat {j}$

C

$\left(\frac {k \alpha}{2}\right) \hat {j}$

D

$- 2 (k \alpha) \hat {j}$

Question 182: Palette 182/207

Advance MCQ

Comprehension Passage: Comprehension - 1

A point moves in the plane x, y according to the law $x = kt$ , $y = kt(1 - \alpha t)$ , where k and $\alpha$ are positive constants and t is the time. Based on the above facts, answer the following questions. The moment $t_0$ at which the velocity vector forms an angle $\frac{\pi}{4}$ with the acceleration vector is

A

$\frac{1}{\alpha}$

B

$\frac{1}{2\alpha}$

C

$\frac{2}{\alpha}$

D

$\frac{1}{3\alpha}$

Question 183: Palette 183/207

Advance MCQ

Comprehension Passage: Comprehension - 2

A particle is projected from a point A with velocity $u\sqrt{2}$ at an angle of $45^{\circ}$ with horizontal as shown in figure. It strikes the plane BC at right angles. Based on the above facts, answer the following questions. The velocity of the particle at the time of collision is

A

u

B

$\frac{u}{2}$

C

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

D

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

Question 184: Palette 184/207

Advance MCQ

Comprehension Passage: Comprehension - 2

A particle is projected from a point A with velocity $u\sqrt{2}$ at an angle of $45^{\circ}$ with horizontal as shown in figure. It strikes the plane BC at right angles. Based on the above facts, answer the following questions. The time after which collision takes place is

A

$\frac{u}{g}$

B

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

C

$\frac{u}{g}\left(\frac{\sqrt{3}+1}{\sqrt{3}}\right)$

D

$\left(\frac{\sqrt{3}}{\sqrt{3}-1}\right)\frac{u}{g}$

Question 185: Palette 185/207

Advance MCQ

Comprehension Passage: Comprehension - 3

An oblique projectile is launched from a point O with an initial velocity u that makes an angle $\theta$ with the horizontal. It is observed that the projectile attains a maximum height H at the point $\left(\frac{R}{2}, H\right)$ , where R is the maximum distance from O at which the projectile strikes the ground. Now, if the velocity of the projectile is $\vec{v} = (20\hat{i} + 10\hat{j}) \, \text{ms}^{-1}$ when it is at a height of 15 m above the ground, then based on this information and taking $g = 10 \, ms^{-2}$ , answer the following questions. The launch speed in $\mathrm{ms}^{-1}$ is

A

$20\mathrm{ms}^{-1}$

B

$20\sqrt{2}\mathrm{ms}^{-1}$

C

$40\mathrm{ms}^{-1}$

D

$40\sqrt{2}\mathrm{ms}^{-1}$

Question 186: Palette 186/207

Advance MCQ

Comprehension Passage: Comprehension - 3

An oblique projectile is launched from a point O with an initial velocity u that makes an angle $\theta$ with the horizontal. It is observed that the projectile attains a maximum height H at the point $\left(\frac{R}{2}, H\right)$ , where R is the maximum distance from O at which the projectile strikes the ground. Now, if the velocity of the projectile is $\vec{v} = (20\hat{i} + 10\hat{j}) \, \text{ms}^{-1}$ when it is at a height of 15 m above the ground, then based on this information and taking $g = 10 \, ms^{-2}$ , answer the following questions. The value of $\theta$ (in radian) is

A

$\frac{\pi}{6}$

B

$\frac{\pi}{4}$

C

$\frac{\pi}{3}$

D

$\frac{2\pi}{3}$

Question 187: Palette 187/207

Advance MCQ

Comprehension Passage: Comprehension - 3

An oblique projectile is launched from a point O with an initial velocity u that makes an angle $\theta$ with the horizontal. It is observed that the projectile attains a maximum height H at the point $\left(\frac{R}{2}, H\right)$ , where R is the maximum distance from O at which the projectile strikes the ground. Now, if the velocity of the projectile is $\vec{v} = (20\hat{i} + 10\hat{j}) \, \text{ms}^{-1}$ when it is at a height of 15 m above the ground, then based on this information and taking $g = 10 \, ms^{-2}$ , answer the following questions. The coordinate, where the maximum height is attained is

A

(80, 20) m

B

(20, 40) m

C

(20, 80) m

D

(40, 20) m

Question 188: Palette 188/207

Advance MCQ

Comprehension Passage: Comprehension - 4

Consider the situation shown in the figure. A particle has to be projected from point P in horizontal direction. It is required for the particle to strike the plane AB (see figure). The minimum value of horizontal velocity of particle at point $P$ so that particle may strike the plane $AB$ is

A

$\sqrt{\frac{9}{8}ag}$

B

$\sqrt{\frac{25}{8}ag}$

C

$\sqrt{\frac{1}{2}ag}$

D

$\sqrt{3ag}$

Question 189: Palette 189/207

Advance MCQ

Comprehension Passage: Comprehension - 4

Consider the situation shown in the figure. A particle has to be projected from point P in horizontal direction. It is required for the particle to strike the plane AB (see figure). The time taken by particle in going from point $P$ to plane $AB$ is

A

$4\sqrt{\frac{a}{g}}$

B

$\sqrt{\frac{4a}{g}}$

C

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

D

$\sqrt{\frac{8a}{g}}$

Question 190: Palette 190/207

Advance MCQ

Comprehension Passage: Comprehension - 4

Consider the situation shown in the figure. A particle has to be projected from point P in horizontal direction. It is required for the particle to strike the plane AB (see figure). The maximum value of horizontal velocity of particle at point $P$ so that it may strike the plane $AB$ is

A

$\sqrt{\frac{9}{8}ag}$

B

$\sqrt{\frac{25}{8}ag}$

C

$\sqrt{\frac{1}{2}ag}$

D

$\sqrt{3ag}$

Question 191: Palette 191/207

Advance MCQ

Comprehension Passage: Comprehension - 5

A ball is projected horizontally from a height of 100 m from the ground with a speed of $20 \, ms^{-1}$ . Taking $g = 10 \, ms^{-2}$ and based on the information provided, answer the following questions. The time taken to reach the ground is

A

$\sqrt{5}$ s

B

$2\sqrt{5}$ s

C

$3\sqrt{5}$ s

D

$4\sqrt{5}$ s

Question 192: Palette 192/207

Advance MCQ

Comprehension Passage: Comprehension - 5

A ball is projected horizontally from a height of 100 m from the ground with a speed of $20 \, ms^{-1}$ . Taking $g = 10 \, ms^{-2}$ and based on the information provided, answer the following questions. The horizontal distance it covers before striking the ground is

A

$20\sqrt{5}$ m

B

$40\sqrt{5}$ m

C

$60\sqrt{5}$ m

D

$80\sqrt{5}$ m

Question 193: Palette 193/207

Advance MCQ

Comprehension Passage: Comprehension - 5

A ball is projected horizontally from a height of 100 m from the ground with a speed of $20 \, ms^{-1}$ . Taking $g = 10 \, ms^{-2}$ and based on the information provided, answer the following questions. The angle with the vertical which it strikes the ground is

A

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

B

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

C

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

D

$\tan^{-1}\left(\frac{1}{\sqrt{7}}\right)$

Question 194: Palette 194/207

Advance MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. Select the correct statement from the following

A

The particle will follow a parabolic path to have a projectile motion with an initial velocity of $5 \, ms^{-1}$ and an acceleration of $3 \, ms^{-2}$ acting along -y axis

B

The particle will follow a parabolic path to have a projectile motion with an initial velocity of $6 \, ms^{-1}$ and a constant acceleration of $5 \, ms^{-2}$ acting along -y axis

C

The particle will follow a parabolic path to have a projectile motion with an initial horizontal velocity of $6 \, ms^{-1}$ and a constant acceleration of $10 \, ms^{-2}$ acting along -y axis

D

None of the above statement seems to be correct

Question 195: Palette 195/207

Advance MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. The velocity, of the projectile, along x-axis after 0.2 second is

A

$>6\ ms^{-1}$

B

$<6\ ms^{-1}$

C

$6\ ms^{-1}$

D

zero

Question 196: Palette 196/207

Advance MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. The initial vertical velocity is

A

$6 \, ms^{-1}$

B

$7 \, ms^{-1}$

C

$8 \, ms^{-1}$

D

$10 \, ms^{-1}$

Question 197: Palette 197/207

Advance MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. The velocity of projection of the projectile is

A

$6 \, ms^{-1}$

B

$7 \, ms^{-1}$

C

$8 \, ms^{-1}$

D

$10 \, ms^{-1}$

Question 198: Palette 198/207

Advance MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. The time of ascent of the projectile is

A

0.2 s

B

0.4 s

C

0.6 s

D

0.8 s

Question 199: Palette 199/207

Advance MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. The maximum height attained by the projectile is

A

0.8 m

B

1.6 m

C

2.9 m

D

3.2 m

Question 200: Palette 200/207

Advance MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. The horizontal range of the projectile is

A

3.2 m

B

4.9 m

C

8.7 m

D

9.6 m

Question 201: Palette 201/207

Advance MCQ

Comprehension Passage: Comprehension - 7

The maximum height attained by an oblique projectile is 8 m and the horizontal range is 24 m. Based on the above facts, answer the following questions. The vertical component of the velocity of projection is

A

$\sqrt{g}$

B

$2\sqrt{g}$

C

$3\sqrt{g}$

D

$4\sqrt{g}$

Question 202: Palette 202/207

Advance MCQ

Comprehension Passage: Comprehension - 7

The maximum height attained by an oblique projectile is 8 m and the horizontal range is 24 m. Based on the above facts, answer the following questions. The horizontal component of the velocity of projection is

A

$2\sqrt{g}$

B

$3\sqrt{g}$

C

$4\sqrt{g}$

D

$5\sqrt{g}$

Question 203: Palette 203/207

Advance MCQ

Comprehension Passage: Comprehension - 7

The maximum height attained by an oblique projectile is 8 m and the horizontal range is 24 m. Based on the above facts, answer the following questions. The velocity of projection is

A

$2\sqrt{g}$

B

$3\sqrt{g}$

C

$4\sqrt{g}$

D

$5\sqrt{g}$

Question 204: Palette 204/207

Advance MCQ

Comprehension Passage: Comprehension - 7

The maximum height attained by an oblique projectile is 8 m and the horizontal range is 24 m. Based on the above facts, answer the following questions. The angle of projection is

A

$\cos^{-1}(0.8)$

B

$\sin^{-1}(0.8)$

C

$\tan^{-1}(0.6)$

D

$\cot^{-1}(0.8)$

Question 205: Palette 205/207

Advance MCQ

Comprehension Passage: Comprehension - 8

A particle initially at rest and starting from the origin is moving under the influence of acceleration given by $\vec{a}=\left(6\hat{t}\hat{i}+8\hat{t}\hat{j}\right)\mathrm{ms}^{-2}$ . Based on the above facts, answer the following questions. Velocity of particle at t = 3 s

A

$45 \, ms^{-1}$

B

$40 \, ms^{-1}$

C

$35 \, ms^{-1}$

D

$22 \, ms^{-1}$

Question 206: Palette 206/207

Advance MCQ

Comprehension Passage: Comprehension - 8

A particle initially at rest and starting from the origin is moving under the influence of acceleration given by $\vec{a}=\left(6\hat{t}\hat{i}+8\hat{t}\hat{j}\right)\mathrm{ms}^{-2}$ . Based on the above facts, answer the following questions. Displacement of particle at t = 3 s is

A

28 m

B

30 m

C

35 m

D

45 m

Question 207: Palette 207/207

Advance MCQ

Comprehension Passage: Comprehension - 8

A particle initially at rest and starting from the origin is moving under the influence of acceleration given by $\vec{a}=\left(6\hat{t}\hat{i}+8\hat{t}\hat{j}\right)\mathrm{ms}^{-2}$ . Based on the above facts, answer the following questions. Path of particle will be

A

Straight line

B

Parabola

C

Circle

D

None of these