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

Let the current ' $I$ ' be associated with an electron of charge ' $e$ ' moving in a circular orbit of radius ' $r$ ' with speed ' $v$ ' around the positively charged nucleus. The ratio $\frac{r}{v}$ is

Figure shows the combination of inductances and capacitances. Resonant frequency of the $\mathrm{L}-\mathrm{C}$ circuit is