Two circular loops P and Q of radii ' r ' and ' nr ' are made respectively from a uniform wire. Moment of inertia of loop Q about its axis is 4 times that of loop $P$ about its axis. The value of $n$ is

An observer on sea-coast counts 45 waves in one minute. If the wavelength of the waves is 7 m , then the velocity of the waves will be

A simple pendulum has time period ' $\mathrm{T}_1$ '. The point of suspension is now moved upward according to equation $\mathrm{y}=\mathrm{kt}^2$ where $\mathrm{k}=1 \mathrm{~m} / \mathrm{s}^2$. If new time period is ' $\mathrm{T}_2$ ' then $\mathrm{T}_1^2 / \mathrm{T}_2^2$ will be ( $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

To manufacture a solenoid of length ' $l$ ' and inductance ' $L$ ', the length of the thin wire required is (Diameter of the solenoid is very less than length, $\mu_0=$ permeability of free space)