An infinitely long straight conductor carrying current ' $I$ ' is bent into a shape as shown in figure. The radius of the circular loop is ' $r$ '. The magnetic induction at the centre of the loop at point ' O ' is

( $\mu_0=$ permeability of free space)

Let $R_1, R_2$ and $R_3$ be the radii of three mercury drops. A big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is

Fundamental frequency of sonometer wire is ' $n$ '. If the tension and length are increased 3 times and diameter is increased twice, the new frequency will be

Moment of inertia of a solid sphere about its diameter is 'I'. It is then casted into 27 small spheres of same diameter. The moment of inertia of each small sphere about its diameter is