Question:
If the period of a simple pendulum of length \(l\) is 5 seconds, then the period of the pendulum of length \(\frac{l}{4}\) is
If the period of a simple pendulum of length \(l\) is 5 seconds, then the period of the pendulum of length \(\frac{l}{4}\) is
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If length becomes \(\frac{1}{4}\) times, period becomes \(\frac{1}{2}\) times.
Updated On: Apr 24, 2026
- \(3 \text{ s}\)
- \(2 \text{ s}\)
- \(2.5 \text{ s}\)
- \(1.5 \text{ s}\)
- \(4 \text{ s}\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Period of simple pendulum: \(T = 2\pi \sqrt{\frac{l}{g}}\). So \(T \propto \sqrt{l}\).
Step 2: Detailed Explanation:
\(\frac{T_2}{T_1} = \sqrt{\frac{l_2}{l_1}} = \sqrt{\frac{l/4}{l}} = \sqrt{\frac{1}{4}} = \frac{1}{2}\)
\(T_2 = \frac{1}{2} \times 5 = 2.5 \text{ s}\)
Step 3: Final Answer:
The new period is \(2.5\) seconds.
Period of simple pendulum: \(T = 2\pi \sqrt{\frac{l}{g}}\). So \(T \propto \sqrt{l}\).
Step 2: Detailed Explanation:
\(\frac{T_2}{T_1} = \sqrt{\frac{l_2}{l_1}} = \sqrt{\frac{l/4}{l}} = \sqrt{\frac{1}{4}} = \frac{1}{2}\)
\(T_2 = \frac{1}{2} \times 5 = 2.5 \text{ s}\)
Step 3: Final Answer:
The new period is \(2.5\) seconds.
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