Question

A mass is kept on a horizontal frictionless surface. It is attached to a string and rotates about a fixed centre at an angular velocity ${\omega }_{\infty }$. If the length of the string and angular velocity are doubled, find the tension in the string which was initially $T_0$.

Answer 1

Angular velocity $={\omega }_{\infty }$

Tension in the string, $T_o=ml{\omega }_{\infty }^2$

If the length of the string and angular velocity are doubled:

New tension, $T^{\prime }=m\times 2l\times 4{\omega }_{\infty }^2$

$⟹T^{\prime }=8ml{\omega }_{\infty }^2$

$⟹T=8T_o$