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MHT CET 2025 (26 Apr, Shift 2) · Spring Systems

Spring Systems question from MHT CET 2025 (26 Apr, Shift 2)

Q35MHT CET 2025 · 26 APR · SHIFT 2Medium

Spring Systems

A mass ' MM ' attached to a horizontal spring executes S.H.M. of amplitude A1A_1. When the mass M passes through its mean position, then a smaller mass ' mm ' is placed over it and both of them move together with amplitude A2A_2. The ratio (A1A2)\left(\frac{A_1}{A_2}\right) is

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Answer: (c)

  1. Momentum conserved at the mean position: Mv=(M+m)v′Mv = (M+m)v'.
  2. A=vω=pk (mass)A = \frac{v}{\omega} = \frac{p}{\sqrt{k\,(\text{mass})}}, and pp is unchanged.
  3. A1A2=M+mM\frac{A_1}{A_2} = \sqrt{\frac{M+m}{M}}, so the answer is (c).
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