Question

Assertion: Frictional forces are conservative forces.
Reason: Potential energy can be associated with frictional forces.
A.A and R are true and R is the correct explanation of A.
B.A and R are true but R is not the correct explanation of A.
C.A is correct but R is wrong.
D.Both A and R are wrong.

Answer 1

Hint: Recall that for a force to be deemed conservative, the work done by the force has to be independent of the path taken by an object and should depend only on the initial and final position of the object. Also, we know that the energy possessed by an object owing to its position is the potential energy. This means that potential energy is associated with conservative forces. Using these definitive statements, establish the kind of force that friction is, following which the validity of both assertion and reason can be obtained.

Complete answer:
Let us begin by prefacing the nature of conservative forces and the energy associated with them.
A conservative force means that the work done by this force in moving any object from one position to the other is independent of the path taken and depends only on the initial and final position of the object.
Now, frictional force is not a conservative since the work done by friction is path-dependent. For example, pushing an object 1m across a rough surface loses less energy as heat than pushing an object 6m across the same surface. Thus, the work done by this frictional force (in the form of energy loss in this case) is dependent on the path taken.
This brings us to the principle of conservation of mechanical energy which states that the total mechanical energy of the system remains constant as long as the only forces acting on the system are conservative forces.
Thus, a non-conservative force such as friction removes energy from the system such that the amount of mechanical energy in the system is not conserved.
This means that the Assertion is incorrect.
Now, the work done by a conservative force depends on the initial and final position of the object. We know that the energy possessed by an object by virtue of its position is the potential energy.
Thus, potential energy is associated with conservative only, and since frictional forces are non-conservative forces, potential energy is not associated with them.
This means that even the Reason is incorrect, let alone a proper justification.

Therefore, the correct choice would be: D. Both A and R are wrong.

Note:
It is important to remember the distinction between conservative and non-conservative forces. A conservative force “conserves” the energy of the system by not spending it on collateral processes, whereas a non-conservative force does not shy away from energy expenditures on such processes via heat, sound, light, etc.
The work done by a conservative force is independent of the path taken and depends only on the initial and final position of the body whereas the work done by a non-conservative force is dependent on the path taken.
Gravitational and electrostatic forces are examples of conservative forces, whereas, air resistance and friction are examples of non-conservative forces. Note that if the path taken by an object is closed, then the work done by a conservative force is zero.