Assertion: In case of pure rolling of a disc on a plank,...

Assertion: In case of pure rolling of a disc on a plank, work done by friction force on the disc must be zero. Reason: In case of pure rolling, point of contact is relatively at rest with respect to the surface.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Key Concepts

Pure Rolling

Pure rolling is a type of motion where a rolling object, such as a disc, rotates about its axis and translates in such a way that the point in contact with the surface is momentarily at rest relative to the surface. This condition, often referred to as the rolling without slipping condition, creates a unique relationship between the translational velocity of the center of mass and the angular velocity of the object.

Static Friction

Static friction is the frictional force that acts at the interface of two surfaces in relative rest with each other, preventing relative sliding. In the context of pure rolling, static friction is responsible for ensuring that the rolling motion is maintained without slipping, even though it doesn't do work because there is no displacement at the point of contact.

Work Done by Friction

Work done by a force is defined as the product of the force and the displacement in the direction of that force. In the case of pure rolling where the point of contact with the surface is momentarily at rest, static friction does not cause displacement at the point of application, and therefore does no net work on the rolling object.

Relative Motion at the Point of Contact

The concept of relative motion at the point of contact is crucial in understanding interactions during rolling motion. Since the point of contact between the rolling object and the surface is instantaneously at rest, any force acting there, such as static friction, does not have an associated displacement, leading to no work being done despite the force's role in maintaining the rolling condition.

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