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).

A moving block having mass $m,$ collides with another stationary block having mass $4\,m$ . The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v,$ then the value of coefficient of restitution $( e)$ will be

Which of the following statement is true?

A ball loses $15.0\%$ of its kinetic energy when it bounces back from a concrete wall. With what speed you must throw it vertically down from a height of $12.4\, m$ to have it bounce back to the same height (ignore air resistance)? ............. $\mathrm{m} / \mathrm{s}$

The bob $A$ of simple pendulum is released when the string makes an angle of $45^o$ with the vertical. It hits another bob $B$ of the same material and same mass kept at rest on the table. If the collision is elastic, then

Explain the total linear momentum is conserved in an elastic collision and also explain the inelastic collision and completely elastic collision.