Perfectly Elastic Collision

Q. A neutron moving at a speed v undergoes a head-on elastic collision with a nucleus of mass number A at rest. The ratio of the kinetic energies of the neutron after and before collision is

1. 
2. 
3. 
4. 

Q.

A pendulum bob of mass M is raised to a heighth and then released. At the bottom of its swing, itpicks up a mass m. To what height will thecombined mass rise?MSM2hm2h(2) (m+M)(1)(m+MmMhmMh(4)(3) (m+M)(m+M)

Q.

The two balls shown in figure are identical, the first moving at a speed $v$ towards right and the second staying at rest. The wall at the extreme right is fixed. Assume all collisions to be elastic. Show that the speeds of the balls remain unchanged after all the collisions have taken place.

1. True

2. False

Q. Answer carefully, with reasons : (a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ? (b) Is the total linear momentum conserved during the short time of an elastic collision of two balls ? (c) What are the answers to (a) and (b) for an inelastic collision ? (d) If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

Q.

Rank the following velocities according to the kinetic energy a particle will have with each

velocity, greatest first: (i) $\overrightarrow{v}=4\hat{i}+3\hat{j}$ (ii) $\overrightarrow{v}=-4\hat{i}+3\hat{j}$ (iii) $\overrightarrow{v}=-3\hat{i}+4\hat{j}$ (iv) $\overrightarrow{v}=3\hat{i}-4\hat{j}$ (v) $\overrightarrow{v}=5\hat{i}$ (vi) $\overrightarrow{v}$ = $5\frac{m}{s}$ at ${30}^{\circ }$ to the horizontal.

1. (i) > (ii) > (iii) > (iv) > (v) > (vi)

2. (i) = (ii) = (iii) = (iv) = (v) = (vi)

3. (i) < (ii) < (iii) < (iv) < (v) < (vi)

4. (i) > (ii) = (iii) = (iv) > (v) > (vi)

Q. A molecule in a gas container hits a horizontal wall with speed 200 m s¯¹ and angle 30° with the normal, and rebounds with the same speed. Is momentum conserved in the collision ? Is the collision elastic or inelastic ?

Q. A swimmer a want to reach directly at point b on the other Bank of the river swims with minimum possible speed with respect to river and reaches directly at point big the width of water is w and river flow with velocity v, then time which swimmer crosses the river is

Q.

$n$ small balls, each of mass $m$, impinge elastically each second on a surface with velocity $u$. The force experienced by the surface will be

1. $mnu$

2. $2mnu$

3. $4mnu$

4. $\frac{1}{2}mnu$

Q. Which of the following potential energy curves in Fig. 6.18 cannot possibly describe the elastic collision of two billiard balls ? Here r is the distance between centres of the balls.

Q. 7.) A bullet when fired at a target with a velocity of 50m/s penetrates 0.5m into it If bullet is fired at a similar target with thickness 0.25m then it will emerge from target with a velocity of

Q. The bob $A$ of a pendulum released from ${30}^o$ to the vertical hits another bob $B$ of the same mass at rest on a table as shown in fig. How high does the bob $A$ rise after the collision ? Neglect the size of the bobs and assume the collision to be elastic.

Q.

A particle of mass $m$ moving with a speed $v$ collide elastically with the end of a uniform rod of mass $M$ and length $L$perpendicularly as shown in the figure. If the particle comes to rest after collision, find the value of $\frac{m}{M}$.$3$

1. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

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

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

4. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.$

Q. Two balls having masses $m_1=5\text{kg}$ and $m_2=10\text{kg}$ moving with velocities $u_1=10\text{m/s}$ and $u_2=5\text{m/s}$ collide elastically. Find the change in momentum of the ball having mass $m_1$ due to collision

1. $110\text{kgm/s}$
2. $90\text{kgm/s}$
3. $-100\text{kgm/s}$
4. $50\text{kgm/s}$

Q. A ball of mass $m$ strikes the fixed inclined plane after falling through a height $h$. If it rebounds elastically, the impulse imparted on the ball is

1. $2m\sqrt{2gh}\cos \theta$
2. $2m\sqrt{gh}\cos \theta$
3. $2m\sqrt{2gh}\sin \theta$
4. $2m\sqrt{2gh}$

Q. A neutron mass $1.67\times {10}^{-27}kg$ moving with a velocity $1.2\times {10}^{7}m{s}^{-1}$ collides head-on with a deuteron of mass $3.34\times {10}^{-27}kg$ initially at rest. If the collision is perfectly elastic, , what would be speed of deuteron after the collision?

1. 
2. 
3. 
4. 

Q. The y-component of a velocity is v m/s and x-component of velocity is root3v m/s. The direction of the body with the y-axis at this instant is

Q.

The track shown in figure is frictionless. The block $B$ of mass $2m$ is lying at rest and the block $A$ of mass $m$ is pushed along the track with some speed. The collision between $A$ and $B$ is perfectly elastic. With what velocity should the block $A$ be started to get the sleeping man awakened?

1. 

2. 

3. 

4. 

Q. The bob A of a pendulum released from 30o to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.15. How high does the bob A rise after the collision? Neglect the size of the bobs and assume the collision to be elastic.

Q. (a) A drop of rain falling down with a constant speed.
(b) A cork of mass $10$ $g$ floating on water.
(c) A kite skillfully held stationary in the sky.
(d) A car moving with a constant velocity of $30$ $km/h$ on a rough road.
(e) A high-speed electron in space far from all material objects, and free of electric and magnetic fields.

Q. In the given figure, a particle $A$ moves along the line $y=30\text{m}$ with a constant velocity of magnitude $3\text{m/s}$ and parallel to the $x-$ axis. At the instant particle $A$ passes the $y-$ axis, the particle $B$ leaves the origin with a zero initial speed and a constant acceleration of magnitude $0.40{\text{m/s}}^2$. What angle $\theta$ between${\overrightarrow{a}}_B$ and the positive direction of the $y-$axis would result in a collision?

1. ${30}^{\circ }$
2. ${15}^{\circ }$
3. ${60}^{\circ }$
4. ${45}^{\circ }$

Q. 19. A ameta block Of mass 10kg is dragged on a rough horizontal surface with constant speed of 5 m/s if the coefficient of kinetic friction between the block and the road is 0.4 then the rate of generation of heat in SI unit is nearly

Q. In an elastic collision of two bodies, the momentum and energy of each body is conserved.

1. True
2. False

Q. A ball falls on an inclined plane of inclination $\theta ={30}^o$ from a height $h=10\text{m}$ above the point of impact and makes a perfectly elastic collision. Find the maximum height attained by the ball, perpendicuar to wedge surface. (take $g=10{\text{m/s}}^2$)

1. $5\sqrt{3}\text{m}$
2. $5\text{m}$
3. $10\text{m}$
4. $10\sqrt{3}\text{m}$

Q. The bob A of a pendulum released from a height h hits head-on another bob B of the same mass of an identical pendulum initially at rest. What is the result of this collision? Assume the collision to be elastic

1. Bob A and B both move to the left, each attaining a maximum height .
2. Bob A comes to rest at lowest point and bob B move to the left attaining a maximum height h.
3. Bob B moves to the left and bob A moves to the right, each attaining a maximum height .
4. Both bobs come to rest.

Q. a ball is moving with the velocity of 20 m/s collide with the smooth surface as showen in the fig the magnitude of change in velocity of the ball

Q. In an elastic collision
(a) the kinetic energy remains constant
(b) the linear momentum remains constant
(c) the final kinetic energy is equal to the initial kinetic energy
(d) the final linear momentum is equal to the initial linear momentum.

Q.

A heavy steel ball of mass greater than 1 kg moving with a speed of 2 $mse{c}^{-1}$collides head on with a stationary ping-pong ball of mass less than 0.1 gm. The collision is elastic. After the collision the ping-pong ball moves approximately with speed

1. $2mse{c}^{-1}$

2. $4mse{c}^{-1}$

3. $2\times {10}^{4}mse{c}^{-1}$

4. $2\times {10}^{3}mse{c}^{-1}$

Q. Question) A body of mass 5 kg is moving with velocity of $\overrightarrow{V}=(2\hat{i}+6\hat{j})m/s$ at t = 0.5 , After time t = 2 s , Velocity of body is $(10\hat{i}+6\hat{j}),$ then change in momentum of body is what ?

Q.

In an elastic collision of two particles, the momentum of each particle is conserved.

1. True
2. False

Q.

The friction coefficient between the horizontal surface and each of the blocks shown in figure is 0.20. The collision between the blocks is perfectly elastic. Find the separation between the two blocks when they come to rest. Take $g$ = 10 $m/s^2$.

1. 4 cm

2. 3 cm

3. 6 cm

4. 5 cm