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Question

A block of mass M is attached to a horizontal spring and is executing SHM, with amplitude A1. When the mass M passes through its mean position, a smaller mass m is placed over it gently and both of them move together with amplitude A2. The ratio of (A1A2) is
  1. M+mM
  2. M+mM
  3. MM+m
  4. MM+m


Solution

The correct option is B M+mM
Mean position is the equilibrium point.
i.e Fnet=0
So, linear momentum is conserved.
Pi=PfMV1=(M+m)V2
where, V1= velocity of block M at mean position.
V2= velocity of combination of blocks at mean position.
We know, 
V1=A1ω1:V2=A2ω2
where ω1=KM, ω2=KM+m
MA1w1=(M+m)A2w2
MA1KM=(M+m)A2KM+m
A1A2=(KM+m)(M+m)KM×M=M+mM

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