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`U = 2x^(3) - 2x^(3) - 6x^(2) + 5x`, where x is in metres and U is the potential energy which depends on x. Selsct the correct option.A. There are two stable equilibrium positions, at `x = (1 +- (1)/(sqrt6)) m`B. `x = (1 + (1)/(sqrt6)) m` is stable equilibrium position.C. `x = (1 - (1)/(sqrt6)) m` is stable equilibrium position.D. `x = (1 + (1)/(sqrt6)) m` is unstable equilibrium position. |
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Answer» Correct Answer - B `U = 2x^(3) - 6x^(2) + 5x` at eq., `(dU)/(dx) = 6 x^(2) - 12 x + 5 = 0` `x = 1 pm (1)/(sqrt6)` for stable eq., `(d^(2)U)/(dx^(2)) gt 0` `(d^(2)U)/(dx^(2)) = 12 x - 12` `(d^(2)U)/(dx^(2)) gt 0` at `x = 1 + (1)/(sqrt6)` & `(d^(2)U)/(dx^(2)) lt 0` at `x = 1 - (1)/(sqrt6)` |
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