First slide

Stable, Unstable and Neutral equilibrium

Question

A particle can move along x-axis under the action of conservative force and its potential energy at any position is given by $U = (x^{2} - 2 x + 16) J$ . Then the particle is in stable equilibrium at

Moderate

A

$x = 1.5 m$
B

$x = 0.75 m$
C

$x = 1 m$
D

$x = 0.5 m$

Solution

Force acting on the particle, $F = - \frac{d U}{d x} = (- 2 x + 2) N$
At equilibrium, $F = 0 \Rightarrow - 2 x + 2 = 0 \Rightarrow x = 1 m$
Now, $\frac{d^{2} U}{d x^{2}} = - 2$ . So potential energy is minimum at x = 1m.
Hence at x = 1m, the particle is in stable equilibrium.

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