A rigid body rotates about a fixed axis with variable angular velocity $(\alpha-\beta t)$ at time $t$, where $\alpha$ and $\beta$ are constants. The angle through which it rotates before it comes to rest is

The capacity of air filled parallel plate capacitor is $\mathrm{C}_0$. One-half of the space between the plates is filled with a dielectric constant ' K ' as shown in figure. The new capacity becomes $\mathrm{C}_{\mathrm{n}}$. The ratio $\mathrm{C}_{\mathrm{n}}$ to $\mathrm{C}_0$ is

Two black spheres $\mathrm{P} \& \mathrm{Q}$ have radii in the ratio $4: 3$. The wavelength of maximum intensity of radiation are in the ratio $4: 5$ respectively. The ratio of radiated power by P to Q is

A monochromatic ray of light is incident normally on a thin prism of refracting angle A . The ray is deviated through an angle $(1.15)^{\circ}$ in passing through the prism. The ray reflected internally from the second face emerges from the first face making an angle of $(6.3)^{\circ}$ with the incident ray. The refractive index of the prism is