The magnetic field at the centre of a current carrying circular coil of area ' $A$ ' is ' $B$ '. The magnetic moment ( M ) of the coil is ( $\mu_0=$ permeability of free space)

A pipe open at both ends produces a fundamental frequency $n_1$. When the pipe is kept with $\frac{3^{\text {th }}}{4}$ of its length in water, it produces a note of fundamental frequency $\mathrm{n}_2$. The ratio of $\frac{\mathrm{n}_1}{\mathrm{n}_2}$ is

A wind with speed $50 \mathrm{~m} / \mathrm{s}$ blows parallel to the roof of a house. The area of the roof is $300 \mathrm{~m}^2$. Assume that the pressure inside the house is atmospheric pressure. Density of air is $1.2 \mathrm{~kg} / \mathrm{m}^3$. The magnitude of the force exerted by the wind on the roof will be

The pressure ' P ', volume ' V ' and temperature ' T ' of a gas in a jar ' $A$ ' and the gas in other jar ' $B$ ' is at pressure ' 2 P ', volume ' V ' and temperature ' $\frac{T}{4}$ '. Then the ratio of the number of molecules in jar A and jar B will be