Two identical blocks A and B of mass m each are connected to each other by spring of spring constant k. Block B is initially shifted to a small distance `x_(0)` to the left and then released. Choose the correct statements for this problem, after the spring attains it's natural length.

Options

A. Velocity of centre of mass of the system is `1/2 sqrt(k/m) x_(0)`
B. Maximum elongation in spring during the subsequent motion is `(x_(0))/(sqrt(2))`
C. Maximum elongation in spring during the subsequent motion is `x_(0)`
D. Maximum speed of block A during subsequent motion be `sqrt(K/m) x_(0)`

Explanation

`1//2 mv_(0)^(2)=1//2 lx_(0)^(2)`
`v_(cm)=v_(0)//2=1/2sqrt(k/m)x_(0),1//2 kx_(max)^(2)=1/2 (m/2) v_(0)^(2)`
`1//2 kx_(max)^(2)=1/2(1/2kx_(0)^(2))rArr x_(max)=(x_(0))/(sqrt(2))`
`(V_(A))_(max)=(V_(B))_(max)=v_(0)=sqrt(k/m)x_(0)`