Potential energy ( $V$ ) versus distance ( $x$ ) is given by the graph. Rank various regions as per the magnitudes of the force ( $F$ ) acting on a particle from high to low.

Question

Accepted Answer

C. 1. The force acting on a particle equals the negative slope of its potential energy versus position graph.
$$
F = -\frac{dV}{dx}
$$
2. So the magnitude of the force in each region equals the absolute value of the slope between that region's endpoints.
$$
|F| = \left|\frac{V_2-V_1}{x_2-x_1}\right|
$$
3. For region $AB$, from $(0,0)$ to $(1,1)$:
$$
|F_{AB}| = \left|\frac{1-0}{1-0}\right| = 1
$$
4. For region $BC$, from $(1,1)$ to $(2,4)$:
$$
|F_{BC}| = \left|\frac{4-1}{2-1}\right| = 3
$$
5. For region $CD$, from $(2,4)$ to $(4,4)$:
$$
|F_{CD}| = \left|\frac{4-4}{4-2}\right| = 0
$$
6. For region $DE$, from $(4,4)$ to $(6,3)$:
$$
|F_{DE}| = \left|\frac{3-4}{6-4}\right| = 0.5
$$
7. Arrange these magnitudes in descending order.
$$
3 > 1 > 0.5 > 0 \;\Rightarrow\; F_{BC} > F_{AB} > F_{DE} > F_{CD}
$$
Hence, the ranking from high to low is $F_{BC}>F_{AB}>F_{DE}>F_{CD}$, so the answer is **option C**.

Potential energy ( VVV ) versus distance ( xxx ) is given by the graph. Rank various regions as per the magnitudes of the force ( FFF ) acting on a particle from high to low.

Potential energy ( $V$ ) versus distance ( $x$ ) is given by the graph. Rank various regions as per the magnitudes of the force ( $F$ ) acting on a particle from high to low.