Question

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

• 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 1

The Correct Option is B

To determine the direction of the frictional force acting on a cylinder rolling up and down an inclined plane, we need to consider the mechanics of rolling motion.

1. **Physics of Rolling Motion**:

• A cylinder rolling without slipping has both translational and rotational motion.
• The frictional force provides the torque necessary for rotation.

2. **Rolling Up the Incline**:

• When the cylinder rolls up the incline, its translational velocity and rotational motion are directed up the slope.
• Friction acts in the upward direction to prevent slipping and provide necessary torque for upward rotational motion.

3. **Rolling Down the Incline**:

• As the cylinder rolls down, its weight causes it to accelerate downwards, converting potential energy into translational and rotational kinetic energy.
• Friction again acts up the incline to prevent slipping, ensuring it rotates faster with increasing translational speed.

From this analysis, the frictional force consistently acts up the incline during both ascending and descending motions. It helps facilitate the rotational motion required without slipping.

**Conclusion**: Therefore, the correct option is the frictional force acts up the incline while ascending as well as descending.

This understanding aligns with the principles of dynamics and helps confirm that only this solution is possible since the frictional force is directed opposite to the relative motion at the point of contact to prevent slipping.