A plank of mass M is placed on a rough horizontal surface. A man m walks on the plank with an acceleration 'a' while the plank is also acted upon by a horizontal force F whose magnitude and direction can be adjusted to keep the plank at rest.

The coefficient of friction between plank and surface is `mu`. Choose the correct options.
.

Options

A. The maximum value of F to keep plank at rest is `ma + mu(M+m)g`
B. The minimum value of F to keep the plank at rest is `ma-mu(M+m)g`
C. The direction of friction on ground due to plank will always be forward
D. If `F = ma` then friction on man due to plank is also F and friction between plank and ground will be zero

Answer

A, B, D

Explanation

`mu(M+m)`
If `F fr f` then friction due to gravity will be left
`F_(max) = f+mu(M+m)g=ma+mu(M+m)g`
If `F lt f` then friction due to gravity will be right.

`F_(min) = Ma - m(m+M)g`
If `F = ma rArr f =ma =f`