Question

A plank of mass $M$ is held at an angle α to the horizontal on two fixed poles $A$ & $B$ as shown in figure. To keep the plank at rest, a person of mass m moves on the plank with some acceleration (neglect friction between plank & poles). Mark the correct statement for this situation

• A. The direction of friction force ( acting between plank & person) on person is down the plank
• B. Person should move down the plank with an acceleration
  $\frac{(M+m)g\sin \alpha }{m}$ to keep the plank stationary.
• C. Friction force between plank & person is having the magnitude Mgsinα
• D. All of the above

Answer 1

The correct option is D

All of the above

For planck to remain stationary some force must act on planck ot balance the component of gravity force along the length of plank this force can be only provided by friction force between person & planck. The FBD of person & planck are shown

For planck to remain stationary, $f=Mg\sin \alpha$
For person, $Mg\sin \alpha +f=ma$
$\Rightarrow (M+m)g\sin \alpha =ma$
$\Rightarrow a=\frac{(M+m)g\sin \alpha }{m}$