Two blocks A and B of mass `m_A and m_B` respectively are kept in contact on a frictionless table. The experimenter pushes the block A from behind so that the blocks accelerate. If the block A exerts a fore F on the block B, what is the force exerted by the experimenter on A?

Explanation

Let , F= contact force between `m_A and m_B`
and f= force exerted by experimenter
` F+ m_A a f=0 `
`rarr F=f=m_A a `………..i
Now, `m_B.a-F=0`
`rarr F=m_Ba` ……ii.

Form equation i. and equation ii whe have
`rarr f= m_Aa=m_Ba`
`rarr f=m_Ba+m_A a`
`rarr =a (m_B_m_A)`
`rarr f= F/m_B (m_B+m_A)`
` =F(1+ m_A/m_B)`
`[since a= F/m_B]`
`:.` Force exerted by experimenter
`=F(1+m_A/m_B)`.