Question

The potential energy of a particle under a conservative force is given by $U\left(x\right)=\left(x^{2} - 3 x\right)J$ . The equilibrium position of the particle is at:

• A. $x=1.5 \, m$
• B. $x=2m$
• C. $x=2.5m$
• D. $x=3m$

Answer 1

Answer: (A)

$U\left(x\right)=\left(x^{2} - 3 x\right)J$
For a conservative field, Force, $F=-\frac{d U}{d x}$
$\therefore F=-\frac{d}{d x}\left(x^{2} - 3 x\right)=-\left(2 x - 3\right)=-2x+3$
At equilibrium position, $F=0$
$-2x+3=0\Rightarrow x=\frac{3}{2}m=1.5m$