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Physics - W.E.P. Question with Solution | TestHub

PhysicsW.E.P.Conservative force & potential energyMedium2 minQB

PhysicsMediummultiple choice

Passage / Comprehension

Consider the potential energy given by $U (x) = \frac{x ^{4}}{4} - \frac{x ^{3}}{3} - 3 x^{2}$ , where the coefficients of the various powers of x have units such that U has units of joules.

Find the equilibrium points and classify them.

Options:(select one or more)

Answer:

Solution:

$U^{'} = x^{3} - x^{2} - 6 x = x (x - 3) (x + 2) \Rightarrow x = 0, 3, - 2$

$U^{''} = 3 x^{2} - 2 x - 6 : U^{''} (0) = - 6 (< 0, u n s t ab l e), U^{''} (3) = 15 (> 0, s t ab l e), U^{''} (- 2) = 10 (> 0, s t ab l e)$

Only 'x = -2 stable' is correct. Ans. (C)

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Conservative force & potential energy

⏱ 2mℹ️ Source: QB

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