Question

A plank is held at an angle $\alpha$ to the horizontal (Fig) on two fixed supports $A$ and $B$. The plank can slide against the supports (without friction) because of its weight Mg. With what acceleration and in what direction, a man of mass "m" should move so that the plank not move.

• A. $g\sin \alpha (1+\frac{m}{M})$ down the incline
• B. $g\sin \alpha (1+\frac{M}{m})$ down the incline
• C. $g\sin \alpha (1+\frac{m}{M})$ up the incline
• D. $g\sin \alpha (1+\frac{M}{m})$ up the incline

Answer 1

The correct option is B $g\sin \alpha (1+\frac{M}{m})$ down the incline

Man should go down so that man apply frictional force on plank towards up.

Let a be the acceleration of man.

if plank is stationary, then frictional force;

$f=Mg\sin \alpha$ and acceleration of man is $a$.

$a=\frac{mg\sin \alpha +f}{m}=(1+\frac{M}{m})g\sin \alpha$ down the incline.

Option B is correct.