Question

The variation of potential energy $\left(U\right)$ with position $\left(x\right)$ of a system is shown in the figure. The conservative force acting on the system is best represented by

Answer 1

We know that, for a conservative force,
$F=\frac{-dU}{dx}=-$ slope of $U-x$ curve


$\left(i\right)$ Between $O$ and $x_1$,
The slope of the $U-x$ curve is constant and positive.
Thus, $F$ should be constant and negative.
$\left(ii\right)$ Between $x_1$ and $x_2$,
The slope of the $U-x$ curve is zero.
Thus, $F$ should be zero.
$\left(iii\right)$ Between $x_2$ and $x_3$,
The slope of the $U-x$ curve is constant and negative.
Thus, $F$ should be constant and positive.
Based on the above analysis, option $\left(a\right)$ is correct.
$$\begin{array}{c}\text{Why this question ?}\\ \text{Bottom line : If the magnitude of slope is the same for two regions, then equal magnitude forces are}\text{acting in those regions.}\end{array}$$