In the diagram shown, no friction at any contact surface. Initially, the spring has no deformation. What will be the maximum deformation in the spring ? Consider all the strings to be sufficiency large. Consider the spring constant to be `K`.

Answer

`8F//3K`

Explanation

At the time of maximum separation, blocks come in rest in centre of frame.
In `C` frame `/_\K=0`
`W_(|peseudo|)=W_(s)+W_(1F)=W_(2F)=/_\K=0`…….i

Work done by pseudoframe in `C`-frame is zero.
`W_(1F)=Fx_(1C)`
`W_(2F)=2Fx_(2C)`
`0-1/2kx_(max)^(2)+FX_(1C)+2Fx_(2C)=0`.........ii
`1/2k_(max)^(2)=Fx_(1C)+2Fx_(2C)`
`x_(max)=x_(1C)+x_(2C)`
From the concept of centre of mass
`Mx_(1C)=2Mx_(2C)`
`X_(1C)=2x_(2C)`
`:. x_(1C)+2X_(2C)=x_(max)`
`:. 3x_(2C)=x_(max)`
`x_(2C)=x_(max)/3` and `x_(1C)=(2x_(max))/3` Puttng the values in eqn ii
`1/2kx_(max)^(2)=F((2x_(max))/3)+2F(x_(max)/3)`
`1/2kx_(max)=(2F)/3+(2F)/3`
`x_(max)=(8F)/(3K)`