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A block of mass M is attached to a horizontal spring and performs simple harmonic motion with amplitude A1. When it crosses the equilibrium position, a small mass m is gently placed on it so that the two move together thereafter with amplitude A2. What is the ratio A1/A2?

1. (M + m)/M
2. (M/(M + m))^(1/2)
3. ((M + m)/M)^(1/2)
4. (M + m)/m

Correct answer: ((M + m)/M)^(1/2)

Solution

The correct option reflects the conservation of energy and the relationship between the amplitudes before and after the mass m is added. When the small mass m is placed on the block, the total mass increases, which reduces the amplitude of the system due to the increased inertia, leading to the derived ratio of amplitudes as ((M + m)/M)^(1/2).

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