Question

A ball of mass $0.25\text{kg}$ attached to the string of length $1.96\text{m}$ is moving in a horizontal circle. The string will break if the tension in the string is more than $25\text{N}$. What is the maximum angular velocity with which the ball can be moved?

• A. $7.14\text{rad/s}$
• B. $3.92\text{rad/s}$
• C. $1.57\text{rad/s}$
• D. $14.28\text{rad/s}$

Answer 1

The correct option is A $7.14\text{rad/s}$

The tension in the string provides centripetal acceleration to the ball. The relation between the tension $T$ and the angular velocity $\omega$ is given by
$m{\omega }^{2}r=T$,
where $m$ is mass of the ball and $r$ is length of the string. The maximum angular velocity occurs at the maximum tension (breaking tension) in the string i.e.,
${\omega }_{\text{max}}=\sqrt{\frac{T_{\text{max}}}{mr}}=\sqrt{\frac{25}{\left(0.25\right)\left(1.96\right)}}=7.14\text{rad/s}$