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A particle free to move along the x-axis...

A particle free to move along the x-axis has potential energy given as
U(x)=k[1-exp(`-x^2`)]for `-inftyle+infty`, where k is a positive constant of appropriate dimensions. Then :

A

at points away from origin, the particles is in equilibrium

B

for any finite non-zero value of x, there is a force directed away from the origin

C

Its total mechanical energy is `k//2` and it is equal to its equal to its kinetic energy at origin

D

at x=0, the motion of the particle is simple harmonic

Text Solution

Verified by Experts

The correct Answer is:
D
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