Question

A ball of mass 0.5 kg is attached to a string of length 50 cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 N. The maximum possible value of angular velocity of the ball in rad/s is,:

• A. 1600
• B. 40
• C. 1000
• D. 20

Answer 1

The Correct Option is B

The string's tension is proportional to the centripetal force necessary for circular motion:

\[ T = mr\omega^2 \]

Definitions:

• \(T = 400 \, \text{N}\) represents the maximum tension.
• \(m = 0.5 \, \text{kg}\) is the ball's mass.
• \(r = 0.5 \, \text{m}\) is the radius (string length).
• \(\omega\) denotes angular velocity.

Solving the formula for \(\omega\):

\[ \omega = \sqrt{\frac{T}{mr}} = \sqrt{\frac{400}{0.5 \times 0.5}} = \sqrt{\frac{400}{0.25}} = \sqrt{1600} = 40 \, \text{rad/s} \]

The ball's maximum angular velocity is 40 rad/s.