For two simple pendulums first has bob mass M 1 and length l 1 , second has bob mass M 2 and length l 2 . Given M 1 = M 2 a n d l 1 = 2 l 2 . If the vibrational energies of both are same, then which o

Question

For two simple pendulums first has bob mass M 1 and length l 1 , second has bob mass M 2 and length l 2 . Given M 1 = M 2 a n d l 1 = 2 l 2 . If the vibrational energies of both are same, then which of the following is correct?

TestHub · Accepted Answer

Frequency, n = 1 2 π g l Or n ∝ 1 l ∴ n 1 n 2 = l 2 l 1 = l 2 2 l 2 n 1 n 2 = 1 2 ⇒ n 2 = 2 n 1 ⇒ n 2 > n 1 Energy, E = 1 2 m ω 2 a 2 And a 2 ∝ 1 m n 2 ∵ E i s s a m e ∴ a 1 2 a 2 1 = m 2 n 2 2 m 1 n 1 2 Given, n 2 > n 1 a n d m 1 = m 2 ⇒ a 1 > a 2 So, amplitude of B is smaller than A

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