A cylinder rolls up an inclined plane, reaches some height, and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are.

Options

A. up the incline while ascending and down the incline while descending
B. up the incline while ascending as well as descending
C. down the incline while ascending and up the incline while descending
D. down the incline while ascending as well as descending

Answer

B

Explanation

Imagine the cylinder to be moving on a frictionless surface. In both the fases the cases the accelerationof te centre of massof the cylinder is `gsintheta`. This is also the aceleration of the point of contact of the cylinder with the inclined surface. Also no torque (about the centre of cylinder) is actig on the cylinder since we assumed the surface to be frictionless and the forces acting on the cylinder in `mg` and `N` which pass through the centre of the cylinder. Therefore, the frictional force will act in the upward direction in both the cases.

Please note that, in general, we find the acceleration of the point of contact due to translation and rotational motion then find net acceleration opposite direction to that of net acceleration of point of contact.