A block of mass m=2kg of shown dimensions is placed on a plank of mass M = 6Kg which is placed on smooth horizontal plane. The coefficient of friction between the block and the plank is `mu=1/3`. If a horizontal froce F is applied on the plank, then find the maximum value of F (in N) for which the block and the plank move together

Explanation

The block has two tendencies

(i) to slide w.r.t. plank
(ii) to topple over the point O maximum acceleration for sliding

`f_(s)=ma le f_(L)`
`ma le mu mg`
`ale g/3 , a_(max)=g/3`
maximum acceleration for toppling,
N=mg, `f_(s)=ma`
`N.(H/8)=H/2 f_(s) , a_(max)=g/4`
So, the block will topple before sliding. hence `f_(max) =(M+m) g/4`