A small block of mass $m$ slides along a smooth frictional track as shown in the figure. If it starts from rest at $P$ , velocity of block at point $Q$ is

Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of $0.4\, m/s$. It collides head on with the second elastically, the second one similarly with the third and so on. The velocity of the last ball is .............. $\mathrm{m}/ \mathrm{s}$

After head on elastic collision between two balls  of equal masses , one is observed to have a speed of  $3\,\,m/s$  along positive  $x-$ axis and the other has a speed of  $2\,\,m/s$  along negative $x$  axis. The original velocities of the balls are

A vertical spring with force constant $k$ is fixed on a table. A ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

A uniform chain of length $2\,m$ is kept on a table such that a length $60\,cm$ hangs freely from the edge of the table. The total mass of chain is $4\,kg$. The work done in pulling the entire chain on the table is ............. $\mathrm{J}$ (Take $g = 10\,m/s^2$)

Body $A$ of mass $4m$ moving with speed $u$ collides with another body $B$ of mass $2 m$ at rest the collision is head on and elastic in nature. After the collision the fraction of energy lost by colliding body $A$ is