With what frequency should a particle of mass $m$ be rotated so that a body of mass $M$ remains stationary?

$A$ ball of mass $m$ is attached to the free end of a string of length $l$. The ball is moving in a horizontal circular path about the vertical axis as shown in the diagram. The angular velocity $\omega$ of the ball will be ($T =$ Tension in the string).

If a stone of mass $0.5 \ kg$ tied to one end of a wire is whirled in a circular path of radius $2 \ m$ with a speed $40 \ rev/min$ in a horizontal plane,then the tension in the wire is nearly (in $N$)

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 $600 \,rpm$.

$A$ string of length $L$ fixed at one end carries a body of mass $m$ at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string makes an angle $\theta$ with the vertical. The angular frequency of the body is $\omega$. The tension in the string is

$A$ coin placed on a rotating turntable just slips if it is placed at a distance of $4 \ cm$ from the centre. If the angular velocity of the turntable is doubled,it will just slip at a distance of: (in $cm$)