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 :-

- A
$\frac{3}{4}$

- B
$\frac{1}{4}$

- C
$\frac{1}{2}$

- D
$\frac{2}{3}$

Two masses ${m_A}$and ${m_B}$moving with velocities ${v_A}$and ${v_B}$in opposite directions collide elastically. After that the masses ${m_A}$and ${m_B}$move with velocity ${v_B}$and ${v_A}$respectively. The ratio $ \frac{m_A}{m_B} =$

A particle of mass m moving with horizontal speed $6\, m/sec$ as shown in figure. If $m < < M$ then for one dimensional elastic collision, the speed of lighter particle after collision will be

Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (figure). After being displaced by $5^o $ the bob $A$ is released from rest, at $t = 0$ subsequently it collides elastically head-on with the other bob.The graph showing variation in energy of pendulum $A$ with time, for $0 \leqslant t \leqslant T$ (where $T$ is the period of either pendulum).

Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. They fly apart in opposite direction with equal speeds. If their masses are $m_A$ and $m_B$ respectively, then

$A$ ball is of mass $m$, strikes a smooth ground at angle $\alpha$ as shown in figure and is deflected at angle $\beta$. The coefficient of restitution will be