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 ball moving with velocity $2\, m/s$ collides head on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be
A sphere is suspended by a thread of length $\ell $. What minimum horizontal velocity has to be imparted to the sphere for it to reach the height of the suspension
The potential energy of a particle oscillating along $x-$ axis is given as $U =20+ (x - 2)^2$ where $U$ is in $joules$ and $x$ in $meters$ . Total mechanical energy of the particle is $36 \,J$. Maximum kinetic energy of the particle is ............... $\mathrm{J}$
A body of mass $m$ is moving in a circle of radius $r$ with a constant speed $v$. The force on the body is $\frac{{m{v^2}}}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle
A body of mass $m$ moving with velocity $v$ collides head on with another body of mass $2\, m$ which is initially at rest. The ratio of $K.E.$ of the colliding body before and after collision will be