Physics

Problem

A particle moves along the

x

-axis under a potential energy

V(x)=a x^{2}

, where

a>0

is a constant. Which statement about the point

x=0

is correct? a) Force is non-zero at

x=0

and directed toward the origin. b) Force is zero at

x=0

and the equilibrium is stable. c) Force is zero at

x=0

and the equilibrium is unstable. d) Force is zero at

x=0

and the equilibrium is neutral.

Intuitive explanation

The key here is recognizing that $x=0$ is an equilibrium point, and you need to determine its stability by examining the force and potential energy curve. Since $V(x) = ax^2$ is a parabola opening upward with its minimum at the origin, the force $F = -\frac{dV}{dx}$ points back toward $x=0$ from either side—making it a stable equilibrium. Think of it like a ball at the bottom of a bowl: any small displacement creates a restoring force that pulls the particle back.

Intuitive explanation

Browse the problem library