A uniformly charged half ring of a radius ' $R$ ' has linear charge density '$$\sigma$$'. The electric potential at the centre of the half ring is ( $$\epsilon_0=$$ permittivity of free space)

A sonometer wire resonates with 4 antinodes between two bridges for a given tuning fork, when 1 kg mass is suspended from the wire. Using same fork, when mass M is suspended, the wire resonates producing 2 antinodes between the two bridges (distance between two bridges is as before). The value of M is

Let '$$\mathrm{R_1}$$' and '$$\mathrm{R_2}$$' are radii of two mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is

A galvanometer of resistance $$50 \Omega$$ is converted to an ammeter. After shunting, the effective resistance of ammeter is $$2.5 \Omega$$. The value of shunt is