A block of mass 4 kg attached with spring of spring constant 100 N/m is executing SHM of amplitude 0.1m on smooth horizontal surface shown in figure. If another block of mass 5 kg is gently placed on

Question

A block of mass 4 kg attached with spring of spring constant 100 N/m is executing SHM of amplitude 0.1m on smooth horizontal surface shown in figure. If another block of mass 5 kg is gently placed on it, at the instant it passes through the mean position and new amplitude of motion is n − 1 meter then find n/5. Assuming that the blocks always move together.

TestHub · Accepted Answer

At the mean position v ma x ​ = A ω = 0.1 × 4 100 ​ ​ = 0.5 m/s. Momentum conservation when the blocks stick: 4 × 0.5 = 9 v ′ , so v ′ = 9 2 ​ m/s. New amplitude A ′ = ω ′ v ′ ​ = 100/9 ​ 2/9 ​ = 15 1 ​ m = n − 1 , so n = 15 and 5 n ​ = 3 .

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