Question

Assertion (A): When a normal reaction is halved the coefficient of static friction is unchanged.
Reason(R): Limiting friction is directly proportional to the normal reaction.
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true and R is not a correct explanation of A.
(C) A is correct and R is incorrect.
(D) A is incorrect and R is correct.

Answer 1

Hint : In the question, we have given a statement in which states that when a normal reaction is halved the coefficient of static friction is unchanged and for this condition, we have given the reason that limiting friction is directly proportional to the normal reaction.
Here in this question we need to check both the given statements in Assertion and Reason and Comment whether they are both true or not and also whether they are dependent on each other or not.
Complete step by step answer:
Limiting friction is the maximum friction that can be generated between two static surfaces in the contact with each other. Once the force is applied between two surfaces, which are greater than its limiting friction, then the motion will occur where force is dependent upon the nature of the surface. Limiting friction is directly dependent upon the magnitude of normal reaction between two surfaces in contact.
The assertion is true that when the normal reaction is halved the coefficient of static friction is unchanged
And the statement of Reason is true that limiting friction is directly proportional to normal reaction but it is not related to the Assertion.
Because the coefficient of static friction is the manifestation of surface roughness. It is independent of normal reaction.
So, option B is the correct answer.

Note: To understand this question we have to study friction. In this question, they asked about limiting friction. Limiting friction as long as the normal reaction remains the same, the magnitude of limiting friction is independent of the area, and the shape of surfaces that are in contact. The magnitude of the limiting friction F is directly proportional to the normal reaction R between two surfaces that are in contact.