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Question

A block m2 is loaded onto another block m1 placed on a spring of stiffness k as shown in figure. If block m2 is suddenly removed, then magnitude of acceleration of block m1 just after the removal of m2 will be:


  1. m1m2m1+m2g
  2. (m2m1g)
  3. (m1m2g)
  4. m1+m2m1m2


Solution

The correct option is B (m2m1g)
Considering the equilibrium of system, just before removal of m2.

FBD before removal of m2:


Here, x= compression in spring 

kx=(m1+m2)g(i)
 x=(m1+m2)gk

Spring force will remain as it is after removal of m2, because spring will not change its length instantaneously. 

FBD after removal of m2:


Applying Newton's 2nd law on block m1 in direction of acceleration: 

kxm1g=m1a
(m1+m2)gm1g=m1a
(from (i))

a=(m2m1g)

Hence, block m1 will move with acceleration (m2m1g) upwards.

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