$A$ 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 ……………… $\mathrm{sec}$

A particle is made to move from the origin in three spells of equal distances, first along the $x-$ axis, second parallel to $y-$ axis and third parallel to $z-$ axis. One of the forces acting on it is has constant magnitude of $50\,N$ and always acts along the direction of motion. Work done by this force in the three spells of motion are equal and total work done in all the three spells is $300\,J$. The final coordinates of the particle will be

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 force acts on a $3.0\ g$ particle in such a way that the position of the particle as a function of time is given by:

$x = 3t – 4t^2 + t^3$ 

Where $x$ is in metres and $t$ is in seconds. The work done during the first $4\ s$ is …………….. $\mathrm{mJ}$

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