Two particles $$\mathrm{P}$$ and $$\mathrm{Q}$$ performs S.H.M. of same amplitude and frequency along the same straight line. At a particular instant, maximum distance between two particles is $$\sqrt{2}$$ a. The initial phase difference between them is

$$\left[\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)=\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)=\frac{\pi}{4}\right]$$

An electric dipole having dipole moment $$\mathrm{P}=\mathrm{q} \times 2 \ell$$ is placed in a uniform electric field '$$\mathrm{E}$$'. The dipole moment is along the direction of the field. The force acting on it and its potential energy are respectively

The frequencies of three tuning forks $$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are related as $$\mathrm{n}_{\mathrm{A}}>\mathrm{n}_{\mathrm{B}}>\mathrm{n}_{\mathrm{C}}$$. When the forks $$\mathrm{A}$$ and $$\mathrm{B}$$ are sounded together, the number of beats produced per second is '$$n_1$$'. When forks $$\mathrm{A}$$ and $$\mathrm{C}$$ are sounded together the number of beats produced per second is '$$n_2$$'. How may beats are produced per second when forks $$\mathrm{B}$$ and $$\mathrm{C}$$ are sounded together?

The magnetic field intensity 'H' at the centre of a long solenoid having 'n' turns per unit length and carrying a current 'I', when no material is kept in it, is