Two masses `m_(1)` and `m_(2)` are connected by a massless spring of spring constant k and unstreched length l. The masses are placed on a frictionless straight channel – which we consider our x-axis. They are initially at rest at x = 0 and x = l, respectively. At t = 0, a velocity of v0 is suddenly imparted to the first particle. At a later time t0, the centre of mass of the two masses is at-

Options

A. `x=(m_(2)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

`V_(com)=(m_(1)v_(0)+0)/(m_(1)+m_(2)),X_(icom)=(m_(1)(0)+m_(2)(l))/(m_(1)+m_(2))`
Also `X_(com)=((m_(2)l)/(m_(1)+m_(2)))+(m_(1)v_(0)t)/(m_(1)+m_(2))`