A body of mass $M$ is dropped from a height $h$ on a sand floor. If the body penetrates $x\,\,cm$ into the sand, the average resistance offered by the sand of the body is
$Mg\left( {\frac{h}{x}} \right)$
$Mg\left( {1\,+\,\frac{h}{x}} \right)$
$Mgh\,+\,Mgx$
$Mg\left( {1\,-\,\frac{h}{x}} \right)$
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
Two blocks $A$ and $B$ of masses $1\,\,kg$ and $2\,\,kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of $K.E.s$ of both the blocks is
A sphere of mass $m$ travelling at constant speed $v$ strike another sphere of same mass. If coefficient of restitution is $e$, then ratio of velocity of both spheres just after collision is :-
A cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is
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