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
$mg\left( {h + d} \right) - \frac{1}{2}\,k{d^2}$
$mg\left( {h - d} \right) - \frac{1}{2}\,k{d^2}$
$mg\left( {h - d} \right) + \frac{1}{2}\,k{d^2}$
$mg\left( {h + d} \right) + \frac{1}{2}\,k{d^2}$
A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T$. The instantaneous power delivered to the body as a function of time is given by
A particle of mass $m$ moving with velocity $V_0$ strikes a simple pendulum of mass $m$ and sticks to it. The maximum height attained by the pendulum will be
A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is
If the potential energy of a gas molecule is $U = \frac{M}{{{r^6}}} - \frac{N}{{{r^{12}}}},M$ and $N$ being positive constants, then the potential energy at equilibrium must be
A uniform chain of length $2\,m$ is kept on a table such that a length of $60\,\,cm$ hangs freely from the edge of the table. The total mass of the chain is $4\,kg$. What is the work done in pulling the entire chain on the table .............. $\mathrm{J}$