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.

In the diagram shown, no friction at any contact surface. Initially, t

1.	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» Solution :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 valuesin 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)`