Two bodies with masses `m_1` and `m_2(m_1gtm_2)` are joined by a string passing over fixed pulley. Assume masses of the pulley and thread negligible. Then the acceleration of the centre of mass of the system `(m_1+m_2)` is

Options

A. `(g(m_(1)-m_(2)))/((m_(1)+m_(2)))`
B. `(g(m_(1)-m_(2))^(2))/((m_(1)+m_(2)))`
C. `(g(m_(1)+m_(2)))/((m_(1)-m_(2)))`
D. `(g(m_(1)+m_(2)))/((m_(1)-m_(2)))`

Answer

B

Explanation

`(a_(cm))_(y)=(F_(ext))/(M)=((m_(1)+m_(2))g-2T)/(m_(1)+m_(2))to(1)`
But `T=(2m_(1)m_(2)g)/(m_(1)+m_(2))to(2)`