The potential energy of a particle moving along x−axis, 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=78m, particle is at equilibrium
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B
at x=78m, particle is not at equilibrium.
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C
at x=38m, particle is at equilibrium.
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D
at x=38m, particle is not at equilibrium.
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Solution
The correct option is C at x=38m, particle is at equilibrium. Given: U=20+5sin(4πx)
Conservative force, F=−dUdx ⇒F=−20πcos(4πx)
At x=78m:- F=−20πcos(4π.78)=−20πcos7π2 ∴F=0 at x=78m
(∵cos(2n+1)π2=0)
Similarly, at x=38m:- F=−20πcos(4π.38)=−20πcos3π2=0 ∴ Equilibrium at x=78m and x=38m