Question

If the length of a simple pendulum is increased by 44%, the percentage increase in its time period is:

• A. 10%
• B. 20%
• C. 44%
• D. 33%

Hint:

For small changes ($< 10\%$), use $\frac{\Delta T}{T} = \frac{1}{2} \frac{\Delta l}{l}$. For large changes, use the ratio method.

Answer 1

The Correct Option is B

Step 1: Concept
Time period $T \propto \sqrt{l}$.
Step 2: Analysis
New length $l' = 1.44l$. New time period $T' \propto \sqrt{1.44l} = 1.2\sqrt{l} = 1.2T$.
Step 3: Conclusion
Percentage increase $= (1.2 - 1) \times 100 = 20\%$.
Final Answer: (B)