A smooth sphere of mass $M$ moving with velocity $u$ directly collides elastically with another sphere of mass m at rest. After collision their final velocities are $V$ and $v$ respectively. The value of $v$ is

In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is:

Three blocks are initially placed as shown in the figure. Block $A$ has mass $m$ and initial velocity $v$ to the right. Block $B$ with mass $m$ and block $C$ with mass $4m$ are both initially at rest. Neglect friction. All collisions are elastic. The final velocity of block $A$ is

Two bodies $A$ and $B$ collide as shown in Fig. $(i)$ and $(ii)$ Which 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)? ............. $\mathrm{m} / \mathrm{s}$

A body of mass $m$ is at rest. Another body of same mass moving with velocity $ V $ makes head on elastic collision with the first body. After collision the first body starts to move with velocity