Question

The potential energy of a particle is directly proportional to its linear displacement from its mean position. Then, the particle performs a
(A) Retarding straight line motion
(B) Damped SHM
(C) Linear SHM
(D) Angular SHM

Answer 1

In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. The best example of potential energy is a ball sitting at the top of a hill and ripe fruit before it falls.

Complete step by step solution:
To solve such questions, first we need to understand the basic difference between a linear motion and a simple harmonic motion (SHM).
Linear motion, also called rectilinear motion, is one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension. Simple harmonic motion is a special type of periodic motion where the restoring force on the moving object is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position.
The best example of linear motion is an athlete running on a straight track of a park and a bullet shot from a pistol always moves in a straight line. The best example of simple harmonic motion is a pendulum oscillating back and forth from its mean position and bungee jumping.
The expression of potential energy is,
$U = kx$
Thus, the force acting $= - \dfrac{{dU}}{{dx}} = - K$
Hence, we can say that the force is a retarding constant force and the motion of the particle will be in a straight line.
So, the final answer is (A) Retarding straight line motion

Note:
It is not necessary that an object has either kinetic energy or potential energy. Objects can have both kinetic energy and potential energy at the same time. An object can be elevated above the ground (have potential energy) and be moving at the same time (and also have kinetic energy).