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A particle can move along x-axis under the action of conservative force and its potential energy at any position is given by $U = (x^{2} - 2 x + 16) J$ . Then the particle is in stable equilibrium at

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x=1.5 m

x=0.75 m

x=1 m

x=0.5 m

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detailed solution

Correct option is C

Force acting on the particle, F=−dUdx=(−2x+2)NAt equilibrium, F=0⇒−2x+2=0⇒x=1mNow, d2Udx2=−2. So potential energy is minimum at x = 1m.Hence at x = 1m, the particle is in stable equilibrium.

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A particle can move along x-axis under the action of conservative force and its potential energy at any position is given by U=(x2−2x+16)J. Then the particle is in stable equilibrium at

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A particle can move along x-axis under the action of conservative force and its potential energy at any position is given by $U = (x^{2} - 2 x + 16) J$ . Then the particle is in stable equilibrium at