Question

A weightless thread can bear tension up to $3.7 \text{ kg wt}$. A stone of mass $500 \text{ gram}$ is tied to it and revolved in circular path of radius $4 \text{ m}$ in vertical plane. Maximum angular velocity of the stone will be (acceleration due to gravity, $g = 10 \text{ m/s}^2$ )}

• A. 16 rad/s
• B. 4 rad/s
• C. 2 rad/s
• D. 8 rad/s

Hint:

String breaks at the bottom because tension must balance both weight and centripetal force.

Answer 1

The Correct Option is B

Step 1: Concept
In a vertical circle, maximum tension occurs at the lowest point: $T_{max} = mg + mr\omega^2$.

Step 2: Meaning
$T_{max} = 3.7 \text{ kg wt} = 3.7 \times 10 = 37 \text{ N}$. $m = 0.5 \text{ kg}$, $r = 4 \text{ m}$.

Step 3: Analysis
$37 = (0.5 \times 10) + (0.5 \times 4 \times \omega^2) \implies 37 = 5 + 2\omega^2$. $32 = 2\omega^2 \implies \omega^2 = 16$.

Step 4: Conclusion
$\omega = 4 \text{ rad/s}$. Final Answer: (B)