Question

Which one of the following is not a conservative force?
A. Force of friction
B. Magnetic force
C. Gravitational force
D. Electrostatic force

Answer 1

Hint: In conservative force, work done depends only on the initial and final position of the particle. It does not depend on the path followed by the particle. We will consider the given forces and will check which of them are conservative and non-conservative forces, by applying the general definition of a conservative and a non-conservation force.

Complete step-by-step answer:
A conservative force is a type of force which has the property that the total work done in moving an object or a particle between two points is independent of the path taken by the object. A conservative force depends only on the initial and final position of the particle. Conservative force can be assumed as a force that conserves the mechanical energy of a body. For non-conservative forces, the mechanical energy lost during the work has to go somewhere else, by law of conservation of energy.
Gravitational force is a conservative force. The total work done to move an object to and away in the gravitational field does not depend on the path. The amount of work done only depends upon the initial and final distance of the particle from the central body causing the gravitational field.
Magnetic force is a conservative force. The motion of any two electrically charged particles imparts a magnetic force which is a relative phenomenon. The magnetic force is a velocity dependent vector and therefore, it is a conservative force.
Electrostatic force is a conservative force. The work done by an electrostatic force due to the presence of an electric field depends on the initial and final position of the charge and not the path taken by the charge. The electrostatic force is path independent; therefore, it is a conservative force.
Frictional force is a non-conservative force. When a body is moved against friction, work is required to overcome the effect of frictional force. Work done by the frictional depends not only on the initial and final position of the body but also on the length of the path covered. There is no potential energy associated with the frictional force. The kinetic energy lost during the motion of the body under frictional force is converted into heat and sound energy. There is a net loss of mechanical energy in doing work under frictional force; therefore, frictional force is a non-conservative force.
Hence, the correct option is A.

Note: In conservative forces, the work done by an object depends only on the change in potential energy of that object in moving from one point to another. Since potential energy is a state function, it does not depend on the path followed by the object, the work done in a conservative force is independent of the path followed by the object.
Gravitational force and Electrostatic force are central forces. These forces act along a radial line between the two objects and the force depends on the net displacement between two objects. Therefore, these forces are central as well as conservative.