A uniform chain of length $L$ and mass $M$ is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, work required to pull the hanging part on to the table is

When a constant force is applied to a body moving with constant acceleration, power does not remain constant. For power to be constant, the force has to vary with speed as follows

A particle of mass $m$ at rest is acted upon by a force $P$ for a time $t.$ Its kinetic energy after an interval $t$ is

Which one of the following statement does not hold good when two balls of masses ${m_1}$ and ${m_2}$ undergo elastic collision

Two ice skaters $A$ and $B$ approach each other at right angles. Skater $A$ has a mass $30\,kg$ and velocity $1\,m/s$ and skater $B$ has a mass $20\,kg$ and velocity $2\,m/s$ . They meet and cling together. Their final velocity of the couple is ............. $\mathrm{m}/ \mathrm{s}$

In the non-relativistic regime, if the momentum, is increased by $100\%$, the percentage increase in kinetic energy is