Question

Potential energy of a particle along $x-$ axis is given by $U=[-20+(x-2{)}^2]\text{J}$. Force on the particle at $x=0$ is

• A. $6\text{N}$
• B. $4\text{N}$
• C. $8\text{N}$
• D. $10\text{N}$

Answer 1

The correct option is B $4\text{N}$

We know, relation between Potential energy $\left(U\right)$ and Force $\left(F\right)$ is -
$F=-\frac{dU}{dx}$........$\left(1\right)$
Given, $U=-20+(x-2{)}^2$
$\therefore \frac{dU}{dx}=0+2(x-2)$........$\left(2\right)$
Putting $\left(2\right)$ in $\left(1\right)$,
$F=-2(x-2)$
at $x=0$
$F=-2(0-2)=4\text{N}$
Force on the particle at $x=0$ is $4\text{N}$