The acceleration due to gravity at the surface of the planet is same as that at the surface of the earth, but the density of planet is thrice that of the earth. If 'R' is the radius of the earth, the radius of the planet will be

A big water drop is formed by the combination of ' $n$ ' small water droplets of equal radii. The ratio of the surface energy of ' $n$ ' droplets to the surface energy of the big drop is

An inductance of $\frac{300}{\pi} \mathrm{mH}$, a capacitance of $\frac{1}{\pi} \mathrm{mF}$ and a resistance of $20 \Omega$ are connected in series with an a.c. source of $240 \mathrm{~V}, 50 \mathrm{~Hz}$. The phase angle of the circuit is

A simple pendulum of length ' $L$ ' has mass ' $M$ ' and it oscillates freely with amplitude ' $A$ '. At extreme position, its potential energy is