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. (a) `((m_1-m_2)/(m_1+m_2))g`
B. (b) `((m_1-m_2)/(m_1+m_2))^2g`
C. (c) `(m_1g)/(m_1+m_2)`
D. (d) `(m_2g)/(m_1+m_2)`

Answer

B

Explanation

`a="Net pulling force"/"Total mass"`
`=(m_1g-m_2g)/(m_1+m_2)`
`=((m_1-m_2)/(m_1+m_2))g` …(i)
Now, `a_(CM)=(m_1a_1+m_2a_2)/(m_1+m_2)`
`a_(CM)=(m_1(+a)+m_2(-a))/(m_1+m_2)`
`=((m_1-m_2)/(m_1+m_2))a`
Substituting the value of a from Eq. (i) we have,
`a_(CM)=((m_1-m_2)/(m_1+m_2))^2g`