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Question

The potential energy of a particle moving along xaxis, under the action of conservative force, is given by U=20+5sin(4πx), where U is in Joules and x is in metres. Then which of the following is/are true?

A
at x=78 m, particle is at equilibrium
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B
at x=78 m, particle is not at equilibrium.
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C
at x=38 m, particle is at equilibrium.
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D
at x=38 m, particle is not at equilibrium.
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Solution

The correct option is C at x=38 m, particle is at equilibrium.
Given: U=20+5sin(4πx)
Conservative force, F=dUdx
F=20πcos(4πx)

At x=78 m:-
F=20πcos(4π.78)=20πcos7π2
F=0 at x=78 m
(cos(2n+1)π2=0)

Similarly, at x=38 m:-
F=20πcos(4π.38)=20πcos3π2=0
Equilibrium at x=78 m and x=38 m

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