The kinetic energy acquired by a body of mass m is travelling some distance s, starting from rest under the actions of a constant force, is directly proportional to

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 uniform chain of length $L$ and mass $M$ is lying on a smooth table and one third of its length is hanging vertically down over the edge of the table. If $g$ is acceleration due to gravity, work required to pull the hanging part on to the table is

A mass of $0.5\, kg$ moving with a speed of $1.5\, m/s$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $k=50\,N/m$. The maximum compression of the spring would be ................. $\mathrm{m}$

A simple pendulum of mass $200\, gm$ and length $100\, cm$ is moved aside till the string makes an angle of $60^o$ with the vertical. The kinetic and potential energies of the bob, when the string is inclined at $30^o$ to the vertical, are

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