A body of mass 100 gram is tied to a spring of spring constant $8 \mathrm{~N} / \mathrm{m}$, while the other end of a spring is fixed. If the body moves in a circular path on smooth horizontal surface with constant angular speed $8 \mathrm{rad} / \mathrm{s}$ then the ratio of extension in the spring to its natured length will be

A simple pendulum oscillates with an angular amplitude $\theta$. If the maximum tension in the string is 4 times the minimum tension then the value of $\theta$ is

A pendulum bob has a speed $4 \mathrm{~m} / \mathrm{s}$ at its lowest position. The pendulum is 1 m long. When the length of the string makes an angle of $60^{\circ}$ with the vertical, the speed of the bob at that position is (acceleration due to gravity, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$, $\cos 60^{\circ}=0.5$ )