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, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$, $\cos 60^{\circ}=0.5$ )

A wheel initially at rest, begins to rotate about its axis with constant angular acceleration. If it rotates through an angle $\theta_1$ in first 2 s and a further angle $\theta_2$ in the next 2 s , the ratio $\theta_1: \theta_2$ is

For a particle moving in a circle with constant angular speed, which of the following statements is 'false'?

A particle performing uniform circular motion of radius $\frac{\pi}{2} \mathrm{~m}$ makes $x$ revolutions in time $t$. Its tangential velocity is