Question

A 2 kg stone is tied to a 2 m long string and whirled in a circle. If the maximum tension is 64 N, what is the max number of revolutions per minute?

• A. \( 19 \)
• B. \( \frac{60}{\pi} \)
• C. \( \frac{152}{3} \)
• D. \( \frac{120}{\pi} \)

Hint:

Use \( T = m \omega^2 r \) and convert angular speed to revolutions per minute using \( f = \frac{\omega}{2\pi} \).

Answer 1

The Correct Option is D

Tension \( T = m \omega^2 r \Rightarrow 64 = 2 \omega^2 \cdot 2 \Rightarrow \omega = 4 \, \text{rad/s} \)
\[ f = \frac{\omega}{2\pi} = \frac{4}{2\pi} = \frac{2}{\pi} \, \text{rev/sec} \Rightarrow \text{rev/min} = \frac{2 \cdot 60}{\pi} = \frac{120}{\pi} \]