Question

A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the string with respect to the vertical?

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Hint:

When tension is 3 times weight at mean position, bob reaches horizontal position.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
At mean position, \(T = mg + mv^2/l\).
Step 2: Detailed Explanation:
\(3mg = mg + mv^2/l \rightarrow v^2 = 2gl\)
Using energy: \(\frac{1}{2}mv^2 = mgl(1 - \cos\theta)\)
\(\frac{1}{2}m(2gl) = mgl(1 - \cos\theta)\)
\(1 = 1 - \cos\theta \rightarrow \cos\theta = 0 \rightarrow \theta = 90^\circ\)
Step 3: Final Answer:
Maximum displacement is 90°.