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Question

The potential energy of a particle is given by, U=2x3−3x2. (in SI unit) The nature of equilibrium at x=0 & x=1 are

A
Stable, Unstable
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B
Unstable, Stable
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C
Unstable, Stable
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D
Stable, Unstable
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Solution

The correct option is B Unstable, StableIt is given that, potential energy U=2x3−3x2 dUdx=(6x2−6x) Under equilibrium, ⇒6x(1−x)=0 ⇒(x=0) & (x=1) d2Udx2=ddx(6x2−6x)=12x−6 d2Udx2|at x = 0=−6<0→ (Unstable equilibrium) d2Udx2|x=1=6>0→(Stable equilibrium) Hence option B is the correct answer.

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