Two stones of masses $m$ and $2\,m$ are whirled in horizontal circles,the heavier one in a radius $\frac{r}{2}$ and the lighter one in radius $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is

$A$ particle moves in a circle of radius $R$,with a constant speed $v$. Then,during a time interval $t = \pi R / 3v$,which of the following is true?

If at any point on the path of a projectile its velocity is $u$ at an inclination $\alpha$ to the horizontal,then after what time will it move at right angles to its former direction?

$A$ wheel completes $2000$ rotations in covering a distance of $9.5\,km$. The diameter of the wheel is:

The second's hand of a watch has a length of $6\,cm$. The speed of the end point and the magnitude of the difference of velocities at two perpendicular positions will be:

$A$ fighter plane flying horizontally at an altitude of $1.5 \; km$ with a speed of $720 \; km/h$ passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with a muzzle speed of $600 \; m s^{-1}$ to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take $g = 10 \; m s^{-2}$).