Question

Potential energy is not defined for which of the following forces?

• A. Gravitational force
• B. Restoring force
• C. Friction
• D. Electrostatic force

Hint:

For conservative forces, potential energy is defined. Non-conservative forces, like friction, do not have a well-defined potential energy function.

Answer 1

The Correct Option is C

The potential energy of a system is defined for conservative forces. The force associated with potential energy satisfies the condition: \[ dU = - \mathbf{F}_{ci} \cdot d\mathbf{r} \] where \( \mathbf{F}_{ci} \) is a conservative force and \( d\mathbf{r} \) is the displacement vector. The force is called conservative if the work done by the force on a particle moving between two points is independent of the path taken. - Gravitational force is a conservative force, and thus potential energy is defined for it. The gravitational potential energy is given by \( U = -\frac{GMm}{r} \). - Restoring force (such as in Hooke's law for a spring) is also conservative, and potential energy is defined for it. - Electrostatic force is a conservative force, and potential energy is defined for it. The electrostatic potential energy is given by \( U = \frac{kQq}{r} \). - Friction is a non-conservative force. The work done by friction depends on the path taken, and it dissipates energy (as heat). Therefore, potential energy is not defined for friction. Thus, the correct answer is friction.