A pendulum has maximum kinetic energy K 1 . If its length is doubled keeping amplitude same then maximum kinetic energy becomes K 2 . Then the relation between K 1 and K 2 is:

Question

A pendulum has maximum kinetic energy K 1 . If its length is doubled keeping amplitude same then maximum kinetic energy becomes K 2 . Then the relation between K 1 and K 2 is:, K 2 = 2 K 1, K 1 = 2 K 2, K 2 = K 1, K 1 = 4 K 2

MARKS App · Accepted Answer

Maximum kinetic energy = 1 2 mω 2 A 2 ω = g L A = Lθ KE = 1 2 m g L × L 2 θ 2 KE = 1 2 mgLθ 2 If length is doubled K 2 = 1 2 mg 2 L θ 2 [Here we are assuming angular amplitude is same] K 1 K 2 = 1 2 mglθ 2 1 2 mg 2 L θ 2 = 1 2 K 2 = 2 K 1

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