Q. A plank of mass `M` is placed over a smooth inclined plane and a sphere is also placed over the plank.Friction is sufficient between sphere and plank.If plank and sphere are released from rest,the frictional force on the sphere is:-
A) up the plane
B) down the plane
To solve this problem one needs first to find how the sphere will rotate relative to the plank. Since both the sphere and the plank are released from rest and both have the same initial potential energy , both will slide down relative to the plane transforming this potential energy into kinetic energy.
However, because the sphere can rotate and has an inertia momentum only a part of the its initial potential energy will be transformed into kinetic energy, the rest being transformed into rotational energy. (For the plank the things are clear, all the initial potential energy is transformed into kinetic energy.)
Thus the sphere will tend to remain behind the plank in its translational motion, and therefore will start to rotate to the right (up the plane) relative to the plank.
Since the sphere rotates to the right, the friction force between the sphere and the plank must provide the torque to start this rotation.
Therefore the force of friction between the sphere and the plank will be directed down the plane.
The correct answer is B) down the plane.