Question:
Simple pendulum of length \(l\) has a maximum angular displacement \(\theta\). The maximum kinetic energy of the bob is
Simple pendulum of length \(l\) has a maximum angular displacement \(\theta\). The maximum kinetic energy of the bob is
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For small \(\theta\), \(\cos\theta \approx 1 - \frac{\theta^2}{2}\), so KE \(\approx \frac{1}{2}mgl\theta^2\).
Updated On: Apr 23, 2026
- \(mgl(1 - \cos\theta)\)
- \(0.5\ mgl\)
- \(mgl\)
- \(2mgl\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
At maximum displacement, KE = 0, PE = maximum. At mean position, KE = maximum, PE = 0. By energy conservation, maximum KE = loss in PE.
Step 2: Detailed Explanation:
Height gained by bob at angular displacement \(\theta\): \(h = l - l\cos\theta = l(1 - \cos\theta)\).
Loss in PE = \(mgh = mgl(1 - \cos\theta)\). This equals maximum KE.
Step 3: Final Answer:
Thus, maximum KE = \(mgl(1 - \cos\theta)\).
At maximum displacement, KE = 0, PE = maximum. At mean position, KE = maximum, PE = 0. By energy conservation, maximum KE = loss in PE.
Step 2: Detailed Explanation:
Height gained by bob at angular displacement \(\theta\): \(h = l - l\cos\theta = l(1 - \cos\theta)\).
Loss in PE = \(mgh = mgl(1 - \cos\theta)\). This equals maximum KE.
Step 3: Final Answer:
Thus, maximum KE = \(mgl(1 - \cos\theta)\).
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