Physics-
General
Easy
Question
A particle free to move along the 
-axis has potential energy given as 
Where 
is a positive constant of appropriate dimensions. Then
- At points away from origin, the particle is in equilibrium
- For any finite non-zero value of , there is a force directed away from the origin
- Its total mechanical energy is
and it is equal to its kinetic energy at origin
- At
, the motion of the particle is simple harmonic
, there is a force directed away from the origin
and it is equal to its kinetic energy at origin
, the motion of the particle is simple harmonic
The correct answer is: At , the motion of the particle is simple harmonic
If a force acting on an object is a function of position only, it is said to be conservative force and it can be represented by a potential energy (
) function which for one dimensional case satisfies the derivative condition.
Given, 
At 
.
Hence, at equilibrium force exerted on particle is zero.
Also, potential energy of the particle is minimum at 
the potential energy is maximum. Hence, at , the motion of particle is simple harmonic.
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