Two masses `m_(1)`and `m_(2)` are connected by a massless spring of spring constant k and unstretched length l. The masses are placed on a frictionless straight channel, which are consider our x-axis. They are initially at `x = 0` and ` x = l` respectively. At `t = 0,` a velocity `v_(0)` is suddenly imparted to the first particle. At a later time t, the centre of mass of the two masses is at :

Options

A. `x=(m_(1)l)/(m_(1)+m_(2))`
B. `x=(m_(1)l)/(m_(1)+m_(2))+(m_(2)v_(0)t)/(m_(1)+m_(2))`
C. `x=(m_(2)l)/(m_(1)+m_(2))+(m_(2)v_(0)t)/(m_(1)+m_(2))`
D. `x=(m_(2)l)/(m_(1)+m_(2))+(m_(1)v_(0)t)/(m_(1)+m_(2))`

Answer

D

Explanation

`x_(0c)=(m_(1)theta+m_(2)l)/(m_(1)+m_(2))`
`v_(c)=(m_(1)v_(0))/(m_(1)+m_(2)) rArr x_(c) =x_(0c)+v_(c)t`