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Two masses m(1) and m(2) are connected b...

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-

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))`

Text Solution

Verified by Experts

The correct Answer is:
D

`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))`
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