Question

A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles 30° and 60° from vertical (lowest positions) are \(T_1\) and \(T_2\), respectively. Then

• A. \(T_1 = T_2\)
• B. \(T_2>T_1\)
• C. \(T_1>T_2\)
• D. tension in the string always remains the same

Hint:

Tension is maximum at lowest point and decreases as angle increases.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Tension \(T = \frac{mv^2}{l} + mg\cos\theta\).
Step 2: Detailed Explanation:
\(\frac{T_1}{T_2} = \frac{\cos 30^\circ}{\cos 60^\circ} = \frac{\sqrt{3}/2}{1/2} = \sqrt{3}>1\)
So \(T_1>T_2\).
Step 3: Final Answer:
\(T_1>T_2\).