A block of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the maximum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be:

Explanation

Here `M_(1)=4kg and M_(2)=5kg`, The limiting friction between the blocks, `f_(lim)=12N`.
Let F be the force applied on the block B.
The acceleration produced in the system `a=F/(M_(1)+M_(2))=F/(4+5)m//s^(2)=F/9m//s^(2)`
Because of this acceleration, the block A experiences a pseudo force of magnitude `F_(pseudo)=M_(1)a=4xxF/9`, As block A move together with B, `:. F_(pseudo)lef_(lim)`
For maximum value of applied force
`F_(pseudo)=f_(lim) or (4F)/9=12 (or) F=27N`
Thus acceleration of blocks=`27/(4+5)=3m//s^(2)`