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

Two circuits A and B are connected to identical d.c. sources each of e.m.f. 10 volt. Self-inductances of circuits A and B are respectively $\mathrm{L}_{\mathrm{A}}=10 \mathrm{H}$ and $\mathrm{L}_{\mathrm{B}}=10 \mathrm{mH}$. The total resistance of each circuit is $40 \Omega$. The ratio of energy consumed in circuit A and circuit B to build up the current to steady value is

The ratio of the frequencies of two simple pendulums is $4: 3$ at the same place. The ratio of their respective lengths is

A source of sound emits sound wave of frequency ' f ' and moves towards an observer with a velocity $\frac{\mathrm{V}}{3}$ where V is the velocity of sound. If the observer moves away from the source with a velocity $\frac{\mathrm{V}}{5}$ the apparent frequency heard by him will be