At a place, the length of the oscillating simple pendulum is made 1/4 times keeping amplitude same then the total energy will be (a) 2 times (b) 4 times (c) 8 times (d) 16 times

Answer: (b). E = 1/2mω²A² with ω² = g/L, so E = (mgA²)/(2L). For the same amplitude A, E ∝ 1/L. L' = L/4 ⇒ E' = 4E So the answer is (b) 4 times.

At a place, the length of the oscillating simple pendulum is made 1/4… | MHT CET 2025 (26 Apr, Shift 1)

Q20MHT CET 2025 · 26 APR · SHIFT 1Easy

Simple Pendulum

At a place, the length of the oscillating simple pendulum is made $\frac{1}{4}$ times keeping amplitude same then the total energy will be

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Answer: (b)

$E = \frac{1}{2}m\omega^2A^2$ with $\omega^2 = \frac{g}{L}$ , so $E = \frac{mgA^2}{2L}$ .
For the same amplitude $A$ , $E \propto \frac{1}{L}$ .
$L' = \frac{L}{4} \Rightarrow E' = 4E$
So the answer is (b) 4 times.

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