First slide

Concept of potential energy

Question

The force acting on a body moving along x-axis varies with the position of the particle as shown in the fig.
The body is in stable equilibrium at

Moderate

A

$x = x_{1}$
B

$x = x_{2}$
C

both x₁ and x₂
D

neither x₁ nor x₂

Solution

When particle moves away from the origin then at position $x = x_{1}$ force is zero and at $x > x_{1},$ force is positive (repulsive in nature) so particle moves further and does not return back to original position.
i.e. the equilibrium is not stable.
Similarly at position $x = x_{2}$ force is zero and at $x > x_{2},$ force is negative (attractive in nature)
So particle return back to original position i.e. the equilibrium is stable.

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