Collisions
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PHXI06:WORK ENERGY AND POWER

355234 \(N\) identical balls are placed on a smooth horizontal surface. An another ball of same mass collides elastically with velocity \(u\) with first ball of \(N\) balls. A process of collision is thus started in which first ball collides with second ball and the second ball with the third ball so on. The coefficient of restitution for each collision is \(e\). Find speed of \(N\) th ball.

1 \(u(1+e)^{N-1}\)
2 \((1+e)^{N} u\)
3 \(u^{N}(1+e)^{N}\)
4 \(\dfrac{u(1+e)^{N-1}}{2^{N-1}}\)
PHXI06:WORK ENERGY AND POWER

355235 A particle falls from a height \(h\) upon a fixed horizontal plane and rebounds. If \(e\) is the coefficient of restitution, the total distance travelled before rebounding has stopped is

1 \(h\left(\dfrac{1+e^{2}}{1-e^{2}}\right)\)
2 \(\dfrac{h}{2}\left(\dfrac{1+e^{2}}{1-e^{2}}\right)\)
3 \(\dfrac{h}{2}\left(\dfrac{1-e^{2}}{1+e^{2}}\right)\)
4 \(\frac{h}{4}\)
PHXI06:WORK ENERGY AND POWER

355236 A block of mass m moving at a velocity \(v\) collides with another block of mass 2 \(m\) at rest. The lighter block comes to rest after collision. Find the coefficient of restitution

1 \(\dfrac{1}{2}\)
2 1
3 \(\dfrac{1}{3}\)
4 \(\dfrac{1}{4}\)
PHXI06:WORK ENERGY AND POWER

355237 A 1 \(kg\) ball moving at \(12\;m{s^{ - 1}}\) collides with a 2 \(kg\) ball moving in opposite direction at \(24\;m{s^{ - 1}}\). If the coefficient of restitution is \(\dfrac{2}{3}\), then their velocities after the collision are

1 \( - 4\;m{s^{ - 1}}, - 28\;m{s^{ - 1}}\)
2 \( - 28\;m{s^{ - 1}}, - 4m{s^{ - 1}}\)
3 \(4\;m{s^{ - 1}},28\;m{s^{ - 1}}\)
4 \(28\;m{s^{ - 1}},4\;m{s^{ - 1}}\)
PHXI06:WORK ENERGY AND POWER

355238 A ball falls vertically on to a floor, with momentum \(p\), and then bounces repeatedly, the coefficient of restitution is \(e\). The total momentum imparted by the ball to the floor is

1 \(\dfrac{p}{(1-e)}\)
2 \(p\frac{{(1 + e)}}{{(1 - e)}}\)
3 \(p(1 + e)\)
4 \(p\left( {1 + \frac{1}{e}} \right)\)
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PHXI06:WORK ENERGY AND POWER

355234 \(N\) identical balls are placed on a smooth horizontal surface. An another ball of same mass collides elastically with velocity \(u\) with first ball of \(N\) balls. A process of collision is thus started in which first ball collides with second ball and the second ball with the third ball so on. The coefficient of restitution for each collision is \(e\). Find speed of \(N\) th ball.

1 \(u(1+e)^{N-1}\)
2 \((1+e)^{N} u\)
3 \(u^{N}(1+e)^{N}\)
4 \(\dfrac{u(1+e)^{N-1}}{2^{N-1}}\)
PHXI06:WORK ENERGY AND POWER

355235 A particle falls from a height \(h\) upon a fixed horizontal plane and rebounds. If \(e\) is the coefficient of restitution, the total distance travelled before rebounding has stopped is

1 \(h\left(\dfrac{1+e^{2}}{1-e^{2}}\right)\)
2 \(\dfrac{h}{2}\left(\dfrac{1+e^{2}}{1-e^{2}}\right)\)
3 \(\dfrac{h}{2}\left(\dfrac{1-e^{2}}{1+e^{2}}\right)\)
4 \(\frac{h}{4}\)
PHXI06:WORK ENERGY AND POWER

355236 A block of mass m moving at a velocity \(v\) collides with another block of mass 2 \(m\) at rest. The lighter block comes to rest after collision. Find the coefficient of restitution

1 \(\dfrac{1}{2}\)
2 1
3 \(\dfrac{1}{3}\)
4 \(\dfrac{1}{4}\)
PHXI06:WORK ENERGY AND POWER

355237 A 1 \(kg\) ball moving at \(12\;m{s^{ - 1}}\) collides with a 2 \(kg\) ball moving in opposite direction at \(24\;m{s^{ - 1}}\). If the coefficient of restitution is \(\dfrac{2}{3}\), then their velocities after the collision are

1 \( - 4\;m{s^{ - 1}}, - 28\;m{s^{ - 1}}\)
2 \( - 28\;m{s^{ - 1}}, - 4m{s^{ - 1}}\)
3 \(4\;m{s^{ - 1}},28\;m{s^{ - 1}}\)
4 \(28\;m{s^{ - 1}},4\;m{s^{ - 1}}\)
PHXI06:WORK ENERGY AND POWER

355238 A ball falls vertically on to a floor, with momentum \(p\), and then bounces repeatedly, the coefficient of restitution is \(e\). The total momentum imparted by the ball to the floor is

1 \(\dfrac{p}{(1-e)}\)
2 \(p\frac{{(1 + e)}}{{(1 - e)}}\)
3 \(p(1 + e)\)
4 \(p\left( {1 + \frac{1}{e}} \right)\)
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PHXI06:WORK ENERGY AND POWER

355234 \(N\) identical balls are placed on a smooth horizontal surface. An another ball of same mass collides elastically with velocity \(u\) with first ball of \(N\) balls. A process of collision is thus started in which first ball collides with second ball and the second ball with the third ball so on. The coefficient of restitution for each collision is \(e\). Find speed of \(N\) th ball.

1 \(u(1+e)^{N-1}\)
2 \((1+e)^{N} u\)
3 \(u^{N}(1+e)^{N}\)
4 \(\dfrac{u(1+e)^{N-1}}{2^{N-1}}\)
PHXI06:WORK ENERGY AND POWER

355235 A particle falls from a height \(h\) upon a fixed horizontal plane and rebounds. If \(e\) is the coefficient of restitution, the total distance travelled before rebounding has stopped is

1 \(h\left(\dfrac{1+e^{2}}{1-e^{2}}\right)\)
2 \(\dfrac{h}{2}\left(\dfrac{1+e^{2}}{1-e^{2}}\right)\)
3 \(\dfrac{h}{2}\left(\dfrac{1-e^{2}}{1+e^{2}}\right)\)
4 \(\frac{h}{4}\)
PHXI06:WORK ENERGY AND POWER

355236 A block of mass m moving at a velocity \(v\) collides with another block of mass 2 \(m\) at rest. The lighter block comes to rest after collision. Find the coefficient of restitution

1 \(\dfrac{1}{2}\)
2 1
3 \(\dfrac{1}{3}\)
4 \(\dfrac{1}{4}\)
PHXI06:WORK ENERGY AND POWER

355237 A 1 \(kg\) ball moving at \(12\;m{s^{ - 1}}\) collides with a 2 \(kg\) ball moving in opposite direction at \(24\;m{s^{ - 1}}\). If the coefficient of restitution is \(\dfrac{2}{3}\), then their velocities after the collision are

1 \( - 4\;m{s^{ - 1}}, - 28\;m{s^{ - 1}}\)
2 \( - 28\;m{s^{ - 1}}, - 4m{s^{ - 1}}\)
3 \(4\;m{s^{ - 1}},28\;m{s^{ - 1}}\)
4 \(28\;m{s^{ - 1}},4\;m{s^{ - 1}}\)
PHXI06:WORK ENERGY AND POWER

355238 A ball falls vertically on to a floor, with momentum \(p\), and then bounces repeatedly, the coefficient of restitution is \(e\). The total momentum imparted by the ball to the floor is

1 \(\dfrac{p}{(1-e)}\)
2 \(p\frac{{(1 + e)}}{{(1 - e)}}\)
3 \(p(1 + e)\)
4 \(p\left( {1 + \frac{1}{e}} \right)\)
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PHXI06:WORK ENERGY AND POWER

355234 \(N\) identical balls are placed on a smooth horizontal surface. An another ball of same mass collides elastically with velocity \(u\) with first ball of \(N\) balls. A process of collision is thus started in which first ball collides with second ball and the second ball with the third ball so on. The coefficient of restitution for each collision is \(e\). Find speed of \(N\) th ball.

1 \(u(1+e)^{N-1}\)
2 \((1+e)^{N} u\)
3 \(u^{N}(1+e)^{N}\)
4 \(\dfrac{u(1+e)^{N-1}}{2^{N-1}}\)
PHXI06:WORK ENERGY AND POWER

355235 A particle falls from a height \(h\) upon a fixed horizontal plane and rebounds. If \(e\) is the coefficient of restitution, the total distance travelled before rebounding has stopped is

1 \(h\left(\dfrac{1+e^{2}}{1-e^{2}}\right)\)
2 \(\dfrac{h}{2}\left(\dfrac{1+e^{2}}{1-e^{2}}\right)\)
3 \(\dfrac{h}{2}\left(\dfrac{1-e^{2}}{1+e^{2}}\right)\)
4 \(\frac{h}{4}\)
PHXI06:WORK ENERGY AND POWER

355236 A block of mass m moving at a velocity \(v\) collides with another block of mass 2 \(m\) at rest. The lighter block comes to rest after collision. Find the coefficient of restitution

1 \(\dfrac{1}{2}\)
2 1
3 \(\dfrac{1}{3}\)
4 \(\dfrac{1}{4}\)
PHXI06:WORK ENERGY AND POWER

355237 A 1 \(kg\) ball moving at \(12\;m{s^{ - 1}}\) collides with a 2 \(kg\) ball moving in opposite direction at \(24\;m{s^{ - 1}}\). If the coefficient of restitution is \(\dfrac{2}{3}\), then their velocities after the collision are

1 \( - 4\;m{s^{ - 1}}, - 28\;m{s^{ - 1}}\)
2 \( - 28\;m{s^{ - 1}}, - 4m{s^{ - 1}}\)
3 \(4\;m{s^{ - 1}},28\;m{s^{ - 1}}\)
4 \(28\;m{s^{ - 1}},4\;m{s^{ - 1}}\)
PHXI06:WORK ENERGY AND POWER

355238 A ball falls vertically on to a floor, with momentum \(p\), and then bounces repeatedly, the coefficient of restitution is \(e\). The total momentum imparted by the ball to the floor is

1 \(\dfrac{p}{(1-e)}\)
2 \(p\frac{{(1 + e)}}{{(1 - e)}}\)
3 \(p(1 + e)\)
4 \(p\left( {1 + \frac{1}{e}} \right)\)
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PHXI06:WORK ENERGY AND POWER

355234 \(N\) identical balls are placed on a smooth horizontal surface. An another ball of same mass collides elastically with velocity \(u\) with first ball of \(N\) balls. A process of collision is thus started in which first ball collides with second ball and the second ball with the third ball so on. The coefficient of restitution for each collision is \(e\). Find speed of \(N\) th ball.

1 \(u(1+e)^{N-1}\)
2 \((1+e)^{N} u\)
3 \(u^{N}(1+e)^{N}\)
4 \(\dfrac{u(1+e)^{N-1}}{2^{N-1}}\)
PHXI06:WORK ENERGY AND POWER

355235 A particle falls from a height \(h\) upon a fixed horizontal plane and rebounds. If \(e\) is the coefficient of restitution, the total distance travelled before rebounding has stopped is

1 \(h\left(\dfrac{1+e^{2}}{1-e^{2}}\right)\)
2 \(\dfrac{h}{2}\left(\dfrac{1+e^{2}}{1-e^{2}}\right)\)
3 \(\dfrac{h}{2}\left(\dfrac{1-e^{2}}{1+e^{2}}\right)\)
4 \(\frac{h}{4}\)
PHXI06:WORK ENERGY AND POWER

355236 A block of mass m moving at a velocity \(v\) collides with another block of mass 2 \(m\) at rest. The lighter block comes to rest after collision. Find the coefficient of restitution

1 \(\dfrac{1}{2}\)
2 1
3 \(\dfrac{1}{3}\)
4 \(\dfrac{1}{4}\)
PHXI06:WORK ENERGY AND POWER

355237 A 1 \(kg\) ball moving at \(12\;m{s^{ - 1}}\) collides with a 2 \(kg\) ball moving in opposite direction at \(24\;m{s^{ - 1}}\). If the coefficient of restitution is \(\dfrac{2}{3}\), then their velocities after the collision are

1 \( - 4\;m{s^{ - 1}}, - 28\;m{s^{ - 1}}\)
2 \( - 28\;m{s^{ - 1}}, - 4m{s^{ - 1}}\)
3 \(4\;m{s^{ - 1}},28\;m{s^{ - 1}}\)
4 \(28\;m{s^{ - 1}},4\;m{s^{ - 1}}\)
PHXI06:WORK ENERGY AND POWER

355238 A ball falls vertically on to a floor, with momentum \(p\), and then bounces repeatedly, the coefficient of restitution is \(e\). The total momentum imparted by the ball to the floor is

1 \(\dfrac{p}{(1-e)}\)
2 \(p\frac{{(1 + e)}}{{(1 - e)}}\)
3 \(p(1 + e)\)
4 \(p\left( {1 + \frac{1}{e}} \right)\)