Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole $$\overrightarrow P $$ as shown. In this case :

A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as $$\left( {{{{\sigma _0}} \over r}} \right)$$ , then the radius of gyration of the disc about its axis passing through the centre is:

An excited He⁺ ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of wavelength $$\lambda $$, energy $$E = {{1240\,eV} \over {\lambda (in\,nm)}}$$) :

A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin(kx – $$\omega $$t + $$\phi $$). Its snapshot at t = 0 is given in the figure.
For this wave, the phase $$\phi $$ is :