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Question

For shown situation, initially the blocks are at rest and spring is unstretched. Find the maximum elongation in the spring. Neglect friction everywhere.

Here spring constant is K.
  1. F3K
  2. FK
  3. 4F3K
  4. 4FK


Solution

The correct option is C 4F3K
By using reduced mass concept, this system can be reduced to


Where μ=(3m)(6m)3m+6m=2m and
F1= Force on 3m block w.r.t centre of mass of the system.
F1=F2+(3m)acmF1=F2+(3m)⎜ ⎜ ⎜FF29m⎟ ⎟ ⎟F1=F2+F6=23F

Now, from work energy theorem,

2F3xm=12Kx2mxm=4F3K

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