Question

A ball of mass $m$ is connected by a light inextensible cord and is rotated in a circle of radius $R$ on a smooth fixed horizontal table. Initially, the angular velocity of the ball was ${\omega }_0$ and pulling force applied was $T_1$. Now the pulling force is increased by $T_2$, until the radius of rotation of the ball becomes $\frac{R}{4}$. Then find the ratio $\frac{T_2}{T_1}$.

Answer 1

$mass=mRadius=Rangularvelocity={\omega }_{0}Force=T_{1}increasingforce=T_2$

Untill the radius of rotation of the ball becomes $\frac{R}{4}$ Then find$=\frac{T_2}{T_1}$

$\frac{T_2}{T_1}=\frac{R_1}{R_2}{T}_2:T_1=\frac{R}{R/4}=4:1$