A ball P is projected at an angle of $60^\circ$ with the vertical with certain initial speed. Another ball Q of the same mass as that of ball P is projected vertically upwards with the same initial speed as that of P. At the highest point, the ratio of potential energy of ball P to that of ball Q is
$(\sin 30^\circ = 0.5)$

A machine gun fires a bullet of mass 40g with a speed of $600 \text{ ms}^{-1}$. The person holding the gun can bare maximum force of 168N on it. The number of bullets that can be fired from the gun per second is

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $K_c$. Radius of gyration of the same disc about a diamter of the disc is $K_d$. the ratio $K_d : K_c$ is

A solid sphere of radius R and mass M is rotating about its diameter. The moment of intertia of the solid sphere rotating about an axis at a distance $\dfrac{R}{3}$ from the centre and parallel to that diameter is