The coefficient of friction between the board and the floor shown in figure is `mu`. Find the maximum force that the man can exert on the rope so that the board does not slip on the floor.

Explanation

Let T is the force exerted by the man on the rope.
Along vertical direction, `sum F_(v)=0`,
or `N+T=(M+m)g` or `N=(M+m)g-T` The board will not slip over the floor, if `T le f`.
For maximum value of T, we have
`T=f=mu N`
`= mu[(M+m)g-T]`
`= mu(M+m)g-mu T`
or `T=[(mu(M+m)g)/(1+mu)]`