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JEE Main 2011 (AIEEE) · Spring Systems

Spring Systems question from JEE Main 2011 (AIEEE)

Q89JEE Main 2011 · AIEEEMedium

Spring Systems

A mass M,M, attached to a horizontal spring, executes S.H.M.\text{S.H.M.} with amplitude A1.A_1. When the mass MM passes through its mean position then a smaller mass mm is placed over it and both of them move together with amplitude A2.A_2. The ratio of (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})}} with pp unchanged.
  3. A1A2=(M+mM)1/2\frac{A_1}{A_2} = \left(\frac{M+m}{M}\right)^{1/2}, so the answer is (c).
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