A passenger sitting in a train A moving at $$90 \mathrm{~km} / \mathrm{h}$$ observes another train $$\mathrm{B}$$ moving in the opposite direction for $$8 \mathrm{~s}$$. If the velocity of the train B is $$54 \mathrm{~km} / \mathrm{h}$$, then length of train B is:

Three point charges $$\mathrm{q},-2 \mathrm{q}$$ and $$2 \mathrm{q}$$ are placed on $x$-axis at a distance $$x=0, x=\frac{3}{4} R$$ and $$x=R$$ respectively from origin as shown. If $$\mathrm{q}=2 \times 10^{-6} \mathrm{C}$$ and $$\mathrm{R}=2 \mathrm{~cm}$$, the magnitude of net force experienced by the charge $$-2 q$$ is ___________ N.

An atom absorbs a photon of wavelength $$500 \mathrm{~nm}$$ and emits another photon of wavelength $$600 \mathrm{~nm}$$. The net energy absorbed by the atom in this process is $$n \times 10^{-4} ~\mathrm{eV}$$. The value of n is __________. [Assume the atom to be stationary during the absorption and emission process] (Take $$\mathrm{h}=6.6 \times 10^{-34} ~\mathrm{Js}$$ and $$\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$$ )

A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be _________ rad s$$^{-2}$$.