The potential energy of a particle varies with position x according to the relation U x = 2 x 4 - 27 x . The point x = 3 2 is point of

Question

The potential energy of a particle varies with position x according to the relation U x = 2 x 4 - 27 x . The point x = 3 2 is point of, unstable equilibrium, stable equilibrium, neutral equilibrium, none of these

MARKS App · Accepted Answer

U = 2 x 4 - 27 x dU dx = 8 x 3 - 27 At x = 3 2 , dU dx = 0 , therefore it is an equilibrium position. d 2 U dx 2 = 24 x 2 At x = 3 2 , d 2 U dx 2 > 0 , therefore it is a stable equilibrium position.

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