Consider the condition shown in the figure. Pulley is massless and frictionless, springs are massless. Both the blocks are released with the springs in their natural lengths. Choose the correct options.

Options

A. Maximum elongation in the spring `S_(1)` is `(4m_(1)m_(2)g)/(K_(1)(m_(1)+m_(2)))`
B. Maximum elongation in the spring `S_(1)` is `(4m_(1)m_(2)g)/(K_(2)(m_(1)+m_(2)))`
C. If `m_(1)=m_(2)` both the blocks will come to instantaneous rest simultaneously.
D. If `K_(1)=K_(2)` both the blocks will come to instantaneous rest simultaneously.

Explanation

Above situation can be represented as

Now at maximum elongation of spring is x
`a_(2//1)=2 g-k_(eq)xx(1/(m_(1))+1/(m_(2)))`
`vdv=[2g-k_(eq)xx((m_(1)+m_(2))/(m_(1)m_(2)))]dx`
`rArr x_(max)=(4m_(1)m_(2)g)/(K_(eq)(m_(1)+m_(2)))`
`k_(1) x_(1)=k_(2)x_(2)=k_(eq)x`