Question

A cylinder is executing pure rolling without slipping with a fixed velocity on a plank, whose upper surface is rough enough, but the lower surface is smooth. The plank is kept at stationary on a smooth horizontal surface by the application of an external force$F$. Choose the correct alternative for this condition.

A. The direction of $F$ is towards right.
B. the direction $F$ is towards the left.
C. The value of $F$ is zero.
D. the direction of $F$ depends on the ratio of the alternative masses of disc and plank.

Answer 1

In this question, it is mentioned that there is no slipping between the plank and the lower surface. No slipping means that the point A will not be slipping over the plank.
Therefore, there is no frictional force acting on the disc and the plank. These all may help you to solve this question.

Complete answer:
First of all let us take a look at the frictional force in general. Frictional Force is defined as the force produced by the two surfaces that are in contact and slide against each other. These forces are primarily due to the texture of the surface and the quantity of force required together. The angle and position of the body is affected by the volume of frictional force. Here it is mentioned that there is no slipping which means the point A will be not slipping over the plank. Therefore, no frictional force will be there acting on the disc and the plank. Hence the force $F$ is not required to overcome any other forces such as $f=0$. Therefore the plank will be at rest itself.

So, the correct answer is “Option C”.

Note:
Rolling resistance is also known as the rolling friction or rolling drag. This is the force opposing the motion when an object rolls on a surface. It is mainly developed because of the non-elastic effects.