A disc at rest is subjected to a uniform angular acceleration about its axis. Let $\theta$ and $\theta_1$ be the angle made by the disc in $2^{\text {nd }}$ and $3^{\text {rd }}$ second of its motion. The ratio $\frac{\theta}{\theta_1}$ is

A body moves along a circular path of radius 15 cm . It starts from a point on the circular path and reaches the end of diameter in 3 second, The angular speed of the body in $\mathrm{rad} / \mathrm{s}$ is

A wheel of radius 1 m rolls through $180^{\circ}$ over a plane surface. The magnitude of the displacement of the point of the wheel initially in contact with the surface is.

The string of pendulum of length ' $L$ ' is displaced through $90^{\circ}$ from the vertical and released. Then the maximum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is ( $\mathrm{m}=$ mass of pendulum, $\mathrm{g}=$ acceleration due to gravity)