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 tension in the string is related to the centripetal force required for circular motion:

\[ T = mr\omega^2 \]

where:

• \(T = 400 \, \text{N}\) is the maximum tension.
• \(m = 0.5 \, \text{kg}\) is the mass of the ball.
• \(r = 0.5 \, \text{m}\) is the radius (length of the string).
• \(\omega\) is the angular velocity.

Rearranging the formula to solve for \(\omega\):

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

Thus, the maximum possible angular velocity of the ball is 40 rad/s.