$A$ stone of mass $16 \, kg$ is attached to a string $144 \, m$ long and is whirled in a horizontal circle. The maximum tension the string can withstand is $16 \, N$. The maximum velocity of revolution that can be given to the stone without breaking it will be ....... $m/s$.

Two masses $M$ and $m$ are attached to a vertical axis by weightless threads of combined length $l$. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity $\omega$. If the tensions in the threads are the same during motion,the distance of $M$ from the axis is

$A$ train is running at $20 \, m/s$ on a railway line with a radius of curvature of $40,000 \, m$. The distance between the two rails is $1.5 \, m$. For safe running of the train,the elevation of the outer rail over the inner rail is ...... $mm$ $(g = 10 \, m/s^2)$.

Find the centripetal force acting on a coin weighing $0.1 \,kg$ placed $0.1 \,m$ from the centre on a gramophone disc rotating at $600 \,rpm$.

$A$ particle of mass $m$ is rotating in a plane in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is:

$A$ particle moves with constant angular velocity in a circular path of a certain radius and is acted upon by a certain centripetal force $F$. If the angular velocity is doubled,keeping the radius the same,the new force will be