The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value then its new time period will become

A simple pendulum with bob of mass m and conducting wire of length $L$ swings under gravity through an angle $\theta$. The component of earth's magnetic field in the direction perpendicular to swing is B . Maximum e.m.f. induced across the pendulum is ( $\mathrm{g}=$ acceleration due to gravity)

In a cyclic process, work done by the system is

A metal sphere cools at a rate of $1.5^{\circ} \mathrm{C} / \mathrm{min}$ when its temperature is $80^{\circ} \mathrm{C}$. When the temperature of the sphere is $40^{\circ} \mathrm{C}$, its rate of cooling is $0.3^{\circ} \mathrm{C} / \mathrm{min}$. The temperature of the surrounding $\left(\theta_0\right)$ is