Consider the arrangement shown. The system is released from rest and the string connecting two blocks is burnt, simultaneously. Maximum extension in the spring (initially releaxed) during the subsequent motion is

Options

A. `(2mg)/(k)`
B. `(4mg)/(k)`
C. `(8mg)/(k)`
D. `(16mg)/(k)`

Explanation

acceleration from cm frame `=(3mg)/(18m)=(g)/(6)`

`4mgx_(2)+4mg x_(1)-(1)/(2)k(x_(1)+x_(2))^(2)=0`
`rArrx_(1)+x_(2)=(16mg)/(k)`