Two spherical conductors of capacities $$3 \mu \mathrm{F}$$ and $$2 \mu \mathrm{F}$$ are charged to same potential having radii $$3 \mathrm{~cm}$$ and $$2 \mathrm{~cm}$$ respectively. If '$$\sigma_1$$' and '$$\sigma_2$$' represent surface density of charge on respective conductors then $$\frac{\sigma_1}{\sigma_2}$$ is

A circular arc of radius '$$r$$' carrying current '$$\mathrm{I}$$' subtends an angle $$\frac{\pi}{16}$$ at its centre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is $$\left[\mu_0=\right.$$ permeability of free space]

A sound of frequency $$480 \mathrm{~Hz}$$ is emitted from the stringed instrument. The velocity of sound in air is $$320 \mathrm{~m} / \mathrm{s}$$. After completing 180 vibrations, the distance covered by a wave is

A sonometer wire '$$A$$' of diameter '$$\mathrm{d}$$' under tension '$$T$$' having density '$$\rho_1$$' vibrates with fundamental frequency '$$n$$'. If we use another wire '$$B$$' which vibrates with same frequency under tension '$$2 \mathrm{~T}$$' and diameter '$$2 \mathrm{D}$$' then density '$$\rho_2$$' of wire '$$B$$' will be