A plank is held at an angle `alpha` to the horizontal on two fixed supports A and B. The plank can slide against the supports (without friction) because of the weight Mg `sin alpha`. The acceleration and direction in which a man of mass m should move so that the plank does not move are

Options

A. `g sin alpha(1+m/M)` down the incline
B. `g sin alpha(1+M/m)` down the incline
C. `g sin alpha(1+m/M)` up the incline
D. `g sin alpha(1+M/m)` up the incline

Answer

B

Explanation

Free-body diagram of man and plank is given below.

For plank to be at rest, applying Newton's second law to plank along the incline
`Mg sin alpha=f` ..(i)
And applying Newton's second law to man along the incline,
`mg sin alpha+f=ma`...(ii)
`implies a=g sin alpha(1+(M)/(m))` down the incline.