A ball is dropped from height $h$ on a plane. If the coefficient of restitution of the plane is $e$ and if ball hits ground two times, the height upto which it reaches after two jumps, will be

$A$ particle of mass $m$ is released from $a$ height $H$ on $a$ smooth curved surface which ends into a vertical loop of radius $R$, as shown The minimum value of $H$ required so that the particle makes a complete vertical circle is given by

A force of $\left( {2\hat i + 3\hat j + 4\hat k} \right)\,N$ acts on a body for $4\, sec$ and produces a displacement of $\left( {3\hat i + 4\hat j + 5\hat k} \right)\,m.$ The power used is ............. $\mathrm{W}$

A rope is used to lower vertically a block of mass $M$ by a distance $x$ with a constant downward acceleration $\frac{g}{2}$. The work done by the rope on the block is

A mass $m$ moving horizontally with velocity $v_0$ strikes a pendulum of mass $m$. If the two masses stick together after the collision, then the maximum height reached by the pendulum is

The work done by a force $\vec F = (-6x^3\hat i)\, N$, in displacing a particle from $x = 4\, m$ to $x = -2\, m$ is .............. $\mathrm{J}$