Problem 2:
Find The Velocities Of The Colliding Particles After Perfectly Elastic Collision In Term Of Their Initial Velocities Travelling In The Same Straight Line.

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Problem 4:
A Particle Of Mass \( m_1 \) Moving With Velocity \( u_1 \) Collides Head On With A Particle Of Mass \( m_2 \) At Rest Such That After Collision They Travel With Velocities \( v_1 \) And \( v_2 \) Respectively. If The Collision Is Perfectly Elastic One, Show That \( v_2=\frac{2m_1}{m_1+m_2}u_1 \)

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Problem 5:
If A Particle Collides Head On Perfectly Elastic Collision With A Particle Of Same Mass At Rest, Then Show That The Two Particles Exchange Their Velocities.

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Problem 6:
A Particle Of Mass \( m_1 \) Moving With Velocity \( u_1 \) Collides Head-On Collision With A Particle Of Mass \( m_2 \) Moving With Velocity \( u_2 \). If ‘e’ Be The Coefficient Of Restitution, Then Show That The Loss Of The Kinetic Energy As A Result Of The Collision is \( \frac{1}{2}\frac{m_1m_2}{m_1+m_2}{(u_1-u_2)}^2(1-e^2) \)

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Problem 7:
A Particle Of Mass ‘ \( m \)’ Moving With Velocity ‘ \( V \)’ Collides Head-On With Another Particle Of Mass ‘ \( 2m \)’, Which Was At Rest. If The Collision Is Perfectly Inelastic, Find Out The Velocity Of The Composite Particle.

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Problem 8:
A Neutron Of Mass ‘\( m \)’ Undergoes An Elastic Head-On Collision Nucleus Of Mass ‘\( M \)’, Initially At Rest. By What Function Is The Kinetic Energy Of The Neutron Reduced?

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Problem 9:
A Mass ‘\( m_1 \)’ Travelling With Speed Speed ‘\( u \)’ On A Horizontal Plane Hits Another Mass ‘\( m_2 \)’ Which Is At Rest. If The Coefficient Of Restitution Is ‘\( e \)’, Show That The Loss Of Kinetic Energy Is \( \displaystyle{\frac{1}{2}\frac{m_1m_2}{(m_1+m_2)}(1-e^2)u^2} \)

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Problem 10:
A Gun Fires A Bullet Of Mass ‘\( m \)’ With Horizontal Velocity ‘\( v \)’ Into A Block Of Wood Of Mass ‘\( M \)’ Which Rest At A Horizontal Friction Less Plane, If The Bullet Becomes Embedded In The Wood, (i) Determine The Subsequent Velocity Of The System And (ii) Find The Loss In The Kinetic Energy.

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Problem 11:
A Particle Of Mass ‘\( m \)’ Moving With Velocity ‘\( u \)’ Collides With A Target Particle Of Unknown Mass Initially At Rest. If After The Collision The Target Particles Travels Forward With A Velocity ‘\( \frac{u}{3} \)’, While The Incident Particle Moves Backward With A Velocity ‘\( \frac{2u}{3} \)’, Find The Mass Of The Target Particle.

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Problem 12:
A Particle Is Dropped Vertically On To A Fixed Horizontal Plane. If It Hits The Plane With Velocity ‘\( u \)’, Show That It Rebounds With Velocity (\( -eu \)).

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Problem 13:
A Particle Dropped Vertically On A Fixed Horizontal Plane From Rest At A Height ‘H’ Above The Plane. Prove That The Total Theoretical Distance Traveled By The Particle Before Coming To Rest Is \( \displaystyle{\frac{1+e^2}{1-e^2}H} \).

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Problem 14:
A Particle Is Dropped Vertically On To A Fixed Horizontal Plane From Rest At A Height ‘H’ From The Plane. Prove That The Total Theoretical Time Taken By The Particle To Come To Rest Is
\( \displaystyle{\sqrt{\frac{2H}{g}}\cdot{\frac{1+e}{1-e}}} \).

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