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Physics · WORK, ENERGY AND POWER
हिन्दीA force \( F(x) = -(kx - ax^3) \) acts on a particle of mass \( m \), where \( k \) and \( a \) are positive constants. The potential energy \( V(x) \) is defined such that \( V(0) = 0 \). The non-zero positions of stable equilibrium are:
Correct answer · Option 2
No non-zero stable equilibrium points exist
Explanation
Equilibrium: \( F(x) = -x(k - ax^2) = 0 \implies x=0 \) or \( x = \pm \sqrt{k/a} \). We have \( \frac{dF}{dx} = -k + 3ax^2 \). At \( x = \pm \sqrt{k/a} \), \( \frac{d^2V}{dx^2} = -\frac{dF}{dx} = k - 3a(k/a) = -2k < 0 \), which represents unstable equilibrium. Thus, no non-zero stable equilibrium points exist.
