A body dropped from a height $1\,m$ on a floor rises to a height $25\,cm$ after first  rebound. The coefficient of restitution is :-

Two small balls are fixed at the ends of a light rigid rod of length $0.4\  m$.The system is released from height $h = 5\  m$ with rod horizontal. The balls collide with the horizontal surface and rebound . The coefficient of restitution between $A$ and ground is $0. 6$ and that between $B$ and ground is $0.4$ . Find angular speed (in $rad/s$) just after the collision. Taking acceleration of free fall $10\ m/s^2$

A bullet of mass $0.012\;kg$ and hortzontal speed $70\; m s ^{-1}$ strikes a block of wood of mass $0.4\; kg$ and instantly comes to rest with respect to the block. The block is suspended from the celling by means of thin wires. Calculate the height to which the block rises. Also, estimate the amount of heat produced in the block.

In the elastic collision of objects

Two equal masses ${m_1}$ and ${m_2}$ moving along the same straight line with velocities $+ 3 \,m/s$ and $-5\, m/s$ respectively collide elastically. Their velocities after the collision will be respectively

A body $A,$ of mass $m=0.1\; kg$ has an initial velocity of $3 \hat{\mathrm{i}}\; \mathrm{ms}^{-1} .$ It collides elastically with another body, $\mathrm{B}$ of the same mass which has an initial velocity of $5 \hat{\mathrm{j}} \;\mathrm{ms}^{-1}$. After collision. A moves with a velocity $\overline{\mathrm{v}}=4(\hat{\mathrm{i}}+\hat{\mathrm{j}})$. The energy of $\mathrm{B}$ after collision is written as $\frac{\mathrm{x}}{10} \;\mathrm{J}$ The value of $x$ is