Line of Impact

Q. A block of mass $m=1\text{kg}$ slides with velocity $v=6{\text{ms}}^{-1}$ on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about $\text{O}$ and swings as a result of the collision, making angle $\theta$ before momentarily coming to rest. If the rod has mass $M=2\text{kg}$ and length $l=1\text{m}$, the value of $\theta$ is approximately-

$[$Take $g=10{\text{ms}}^{-2}]$

1. ${63}^{\circ }$
2. ${55}^{\circ }$
3. ${69}^{\circ }$
4. ${49}^{\circ }$

Q. A rod of mass $M$ and length $L$ is lying on a horizontal frictionless surface. A particle of mass $m$ travelling along the surface hits at one end of the rod with a velocity $u$ in a direction perpendicular to the rod. The collision is completely elastic. After collision, the particle comes to rest. The ratio of masses $\left(\frac{m}{M}\right)$ is $\frac{1}{x}$. The value of ${}^{\prime }{x}^{\prime }$ will be ______.

Q. Two balls of identical masses undergo perfectly elastic oblique collsion. One of the balls (Ball 1) is initially at rest while the other (Ball 2) is moving with velocity $v$. After the collisions, what angle will the final velocities of the balls make with each other?

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. A ball of mass $m$ strikes a rigid wall with speed $u$ and rebounds with the same speed. The impulse imparted to the ball by the wall is

1. $2mu$
2. $mu$
3. zero
4. $-2mu$

Q.

Figure (10 - E15) shows a small spherical ball of mass m rolling down the loop track. The ball is released on the linear portion at a vertical height H from the lowest point. The circular part shown has a radius R. (a) Find the kinetic energy of the ball when it is at a point A where the radius makes an angle $\theta$ with the horizontal. (b) Find the radial and the tangential accelerations of the centre when the ball is at A.

Q. A stone is projected from the ground and hits a smooth vertical wall after $1\text{s}$ and again fall back on the ground as shown in the figure. The time taken by the stone to reach the ground after the collision is $3\text{s}$. The maximum height reached by the same stone if the vertical wall is not present will be
(Take $g=10{\text{m/s}}^2$)

1. $14\text{m}$
2. $16\text{m}$
3. $18\text{m}$
4. $20\text{m}$

Q. Two balls of identical masses undergo perfectly elastic oblique collsion. One of the balls (Ball 1) is initially at rest while the other (Ball 2) is moving with velocity $u$. After the collisions, what angle will the final velocities of the balls make with each other?

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q.

A sphere X of mass $2\text{kg}$ is moving to the right at $10{\text{ms}}^{-1}$. Sphere Y of mass $4\text{kg}$is moving to the left at $10{\text{ms}}^{-1}$.The two spheres collide head-on. The ratio of the magnitude of the impulse exerted by X on Y to that exerted by Y on X is

1. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

2. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

3. $1$

4. $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$1$}\right.$

Q. Consider the statements for an oblique collision of two sphere having different masses and initial velocities;

Statement 1: Initial and final velocity of both the spheres perpendicular to line of impact will remain same.
Statement 2: Impulse due to collision of the spheres will not affect initial velocity of sphere along the line of impact.

1. Statement 1 is true but statement 2 is false.
2. Both statements are true.
3. Both statements are false.
4. Statement 2 is true but statement 1 is false.

Q. A steel ball of mass $1\text{kg}$ is released from rest as shown and strikes a ${45}^{\circ }$ inclined surface . If the co-efficient of restitution is $0.8$, the distance $S$, where the ball will strike the horizontal plane at $\text{A}$ will be (approximately)

1. $0.76\text{m}$
2. $0.86\text{m}$
3. $0.66\text{m}$
4. $0.96\text{m}$

Q. In the figure shown, a plate of mass $60\text{gm}$ is at rest and in equilibrium. A particle of mass $m=30\text{gm}$ is released from height $\frac{4.5mg}{K}$ above the plate. The particle hits the plate and sticks to it. If the time interval between the collision of the particle and the time at which it comes to momentary rest for the first time is given by $\frac{\pi }{x}$, then find $x$.
Spring has force constant $1\text{N/m}$. Neglect the duration of collision

Q. At what angle a ball should be thrown with a velocity of $24m{s}^1$ just to cross a wall $16m$ high at a horizontal distance of $32m$ . Given: $g=10m{s}^2$

Q. Consider the statements for an oblique collision of two sphere having different masses and initial velocities;

Statement 1: Initial and final velocity of both the spheres perpendicular to line of impact will remain same.
Statement 2: Impulse due to collision of the spheres will not affect initial velocity of sphere along the line of impact.

1. Statement 1 is true but statement 2 is false.
2. Statement 2 is true but statement 1 is false.
3. Both statements are true.
4. Both statements are false.

Q. A ball A moving with a velocity 5 m/s collides elastically with another identical ball at rest such that the velocity of A makes an angle of ${30}^{\circ }$ with the line joining the centres of the balls. Then:

1. Balls $A$ and $B$ move at right angles after collision
2. Speed of B after collision is $\frac{5}{2}m/s$
3. Kinetic energy is not conserved as the collision is not head-on
4. Speed of A after collision is $\frac{5\sqrt{3}}{2}$ m/s

Q. A ball of mass $0.1$ kg strikes a wall normally with a speed of $30m{s}^{-1}$ and rebounds with a speed of $20m{s}^{-1}$. The impulse of the force exerted by the wall on the ball is

1. $1Ns$
2. $5Ns$
3. $2Ns$
4. $3Ns$

Q. Two balls of identical masses undergo perfectly elastic oblique collsion. One of the balls (Ball 1) is initially at rest while the other (Ball 2) is moving with velocity $u$. After the collisions, what angle will the final velocities of the balls make with each other?

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. Consider the statements for an oblique collision of two sphere having different masses and initial velocities;

Statement 1: Initial and final velocity of both the spheres perpendicular to line of impact will remain same.
Statement 2: Impulse due to collision of the spheres will not affect initial velocity of sphere along the line of impact.

1. Statement 1 is true but statement 2 is false.
2. Statement 2 is true but statement 1 is false.
3. Both statements are true.
4. Both statements are false.

Q. A point mass of $1\text{kg}$ collides elastically with a stationary point mass of $5\text{kg}$. After collision the $1\text{kg}$ mass reverses its direction and moves with a speed of $2{\text{ms}}^{-1}$.
Which of the following statement(s) is/are correct for the system of these two masses?

1. Total momentum of the system after the collision is $3{\text{Kg ms}}^{-1}$
2. Momentum of $5\text{kg}$ mass after the collision is $4{\text{Kg ms}}^{-1}$
3. Total kinetic energy of the system is $4\text{J}$
4. Kinetic energy of the center of mass is $0.75\text{J}$

Q. A ball is thrown at an angle ${53}^{\circ }$ with a velocity of 50 $m{s}^{-1}$. Calculate the difference between the velocities at the two instants when the body is 20 m above the ground

1. 
2. 
3. 
4. 

Q. A ball of mass $m$ strikes a rigid wall with speed $u$ and rebounds with the same speed. The impulse imparted to the ball by the wall is

1. $2mu$
2. $mu$
3. zero
4. $-2mu$

Q. A ball of mass $m$ strikes a rigid wall with speed $u$ and rebounds with the same speed. The impulse imparted to the ball by the wall is

1. $2mu$
2. $mu$
3. zero
4. $-2mu$

Q. The graph above shows the amount of force applied to an initially stationary 20 kg curling rock over time. What is the velocity of the rock after the force has been applied to it?

1. 1.25 m/s
2. 5 m/s
3. 10 m/s
4. 25 m/s
5. 50 m/s

Q. Two balls of same mass are dropped from the same height $h$ on to the floor. The first ball bounces to height $h/4$ after the collision and the second ball to height $h/16$. The impulse applied by the first & second ball on the floor is $I_1$ and $I_2$ respectively. Then:

1. $3I_1=2I_2$
2. $5I_1=6I_2$
3. $I_1=2I_2$
4. $6I_1=5I_2$

Q. A bullet of mass $m$ is fired with the velocity of $50m{s}^{-1}$ at an angle $\theta$ with the horizontal. At the highest point of its trajectory, it collides head-on with a bob of mass $4m$ connected with a massless string of length $l=10/3m$ and gets embedded with the bob. After the collision, the string moves to an angle of ${120}^o$. What is the angle $\theta$

1. ${\cos }^{-1}\left(\frac{1}{5}\right)$
2. ${\sin }^{-1}\left(\frac{4}{5}\right)$
3. ${\cos }^{-1}\left(\frac{5}{4}\right)$
4. ${\sin }^{-1}\left(\frac{5}{4}\right)$