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
$mg\,\left( {h - d} \right) + \frac{1}{2}\,K{d^2}$
$mg\,\left( {h + d} \right) + \frac{1}{2}\,K{d^2}$
$mg\,\left( {h + d} \right) - \frac{1}{2}\,K{d^2}$
$mg\,\left( {h - d} \right) - \frac{1}{2}\,K{d^2}$
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 ............. $\mathrm{m}/ \mathrm{s}$
A bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$, the initial velocity of the bullet will be
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 .............. $\mathrm{m}/ \mathrm{s}$
The length of a spring is $\alpha $ when a force of $4\,N$ is applied on it and the length is $\beta $ when $5\,N$ force is applied. Then the length of spring when $9\,N$ force is applied is
$A$ ball is dropped from height $5m$. The time after which ball stops rebounding if coefficient of restitution between ball and ground $e = 1/2$, is .................. $\mathrm{sec}$