Question

Class 11th Physics:-
Two blocks of mass m and 2m are connected with a spring of spring
constant K and are kept on horizontal frictionless surface. If we impart a
velocity v to block of mass m towards right. The velocity of centre of
mass is ?
Options and figure given in the attachment! Don't Spam!
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Answer 1

Mass of block 1 = m₁

Mass of block 2 = m₂

Velocity of centre of mass = $\frac{m_{2}*v + m_{1} *0 }{m_{1} +m_{2} }$

Velocity = $\frac{m*v + 2m*0}{m+2m}$

v' = $\frac{mv}{3m}$

v' = $\frac{v}{3}$

Therefore, the velocity of centre of mass is $\frac{v}{3}$