A pulley fixed to the ceiling carries a string with blocks of mass `m` and `3m` attached to its ends. The masses of string and pulley are negligible .When the system is released, its center of mass moves with what acceleration

Options

A. 0
B. `g//4`
C. `g//2`
D. `-g//2`

Answer

B

Explanation

`a_(cm)=((m_(1)-m_(2))/(m_(1)+m_(2)))^(2)g=((3m-m)/(3m+m))^(2)g=(g)/(4)`
Aliter :
acceleration of system = `((3m-m)/(4m))g=(g)/(2)`
here `m_(1)=m)`
`a_(1)=(-g)/(2)`
`m_(2)=3m`
`a_(2)=(g)/(2)`
Acceleration of centre of mass
`a_(cm)=(m_(1)a_(1)+m_(2)a_(2))/(m_(1)+m_(2))`
= `(m(-g//2)+3m(g//2))/(4m)=(g)/(4)`