Two particles of masses \(m_1\) and \(m_2\) move with initial velocities \(u_1\) and \(u_2\) respectively. On collision, one of the particles gets excited to a higher level, after absorbing energy \(E\). If the final velocities of particles are \(v_1\) and \(v_2\), then we must have:

On a frictionless surface, a block of mass \(M\) moving at speed \(v\) collides elastically with another block of the same mass \(M\) which is initially at rest. After the collision, the first block moves at an angle \(\theta\) to its initial direction and has a speed \(\frac{v}{3}\). The second block’s speed after the collision will be:

A stone is dropped from a height \(h\). It hits the ground with a certain momentum \(p\). If the same stone is dropped from a height \(100\)% more than the previous height, the momentum when it hits the ground will change by:
1. \(41\)% 
2. \(200\)% 
3. \(100\)% 
4. \(68\)%

A mass \(m\) moving horizontally (along the x-axis) with velocity \(v\) collides and sticks to a mass of \(3m\) moving vertically upward (along the y-axis) with velocity \(2v.\) The final velocity of the combination is:
1. \(\frac{3}{2}v\hat{i}+\frac{1}{4}v\hat{j}\)
2. \(\frac{1}{4}v\hat{i}+\frac{3}{2}v\hat{j}\)
3. \(\frac{1}{3}v\hat{i}+\frac{2}{3}v\hat{j}\)
4. \(\frac{2}{3}v\hat{i}+\frac{1}{3}v\hat{j}\)

A ball moving with velocity 2 ms^-1 collides head-on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in ms^-1) after the collision will be:

1. 0, 1

2. 1, 1

3. 1, 0.5

4. 0, 2

A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is:

1. 100 ms^-1

2. 80 ms^-1

3. 40 ms^-1

4. 120 ms^-1