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:

In the above question, if another body is at rest, then velocity of the compound body after collision is

A ball is thrown with a velocity of $6\, m/s$ vertically downwards from a height $H = 3.2\, m$ above a horizontal floor. If it rebounds back to same height then coefficient of restitution $e$ is $[g = 10\, m/s^2]$

Which one of the following statements does not hold good when two balls of masses $m _1$ and $m _2$ undergo elastic collision

Three objects $A$, $B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m, 2 m$ and $m$, respectively. The object $A$ moves towards $B$ with a speed $9 \mathrm{~m} / \mathrm{s}$ and makes an elastic collision with it. Thereafter, $B$ makes completely inelastic collision with $C$. All motions occur on the same straight line. Find the final speed (in $\mathrm{m} / \mathrm{s}$ ) of the object $\mathrm{C}$.

A body of mass $2\, kg$ moving with a velocity of $6\, m/s$ strikes inelastically another body of same mass at rest. The amount of heat evolved during collision is ............... $\mathrm{J}$