Question

Potential energy of a particle is related to $x$ coordinate by equation $x^2-2x$will be equilibrium at

• A. $x=0.5$
• B. $x=2$
• C. $x=1$
• D. $x=4$

Answer 1

The correct option is C

$x=1$

Step 1: Given Data:

The equation of the potential energy of a particle-

$U=x^2-2x$

Step 2: Formula used:

We know that for stable equilibrium,

$F_{NET}=0$

Also,

$F=-\frac{dU}{dx}$…..(1)

Step 3: Calculating the force:

Using the equation (1)-

$\begin{array}{rcl}F& =& -\frac{dU}{dx}\\ & =& -\frac{d}{dx}\left(x^2-2x\right)\\ & =& -2x+2\end{array}$

We know that for stable equilibrium,

$F_{NET}=0$

Putting the calculated value,

$\begin{array}{rcl}-2x+2& =& 0\\ x& =& 1\end{array}$

Hence option C is the correct answer.