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.

Solution

Physics sir · 3 steps

Force is minus the slope of the V–x graph, so just compare how steep each straight piece is.

1. Force from slope. For a conservative force, F = -dV/dx. So the size of the force in any region equals the magnitude of the slope of the V–x graph there, not the height of V.
2. Read the points. From the grid: A (0, 0), B (1, 1), C (2, 4), D (4, 4), E (6, 3). Each region is a straight line, so its slope is constant.

   Region	Δ V / Δ x	|F|
   AB	(1 - 0)/(1 - 0) = 1	1
   BC	(4 - 1)/(2 - 1) = 3	3, largest
   CD	(4 - 4)/(4 - 2) = 0	0, smallest
   DE	(3 - 4)/(6 - 4) = -1/2	0.5

3. So. From high to low: F_(BC) > F_(AB) > F_(DE) > F_(CD), which is option (a).

The idea to keep. On a potential energy graph, steepness gives force and the sign of the slope gives its direction. A flat part means zero force, however high the potential is.

Answer from the NTA final answer key. Solution by PrepWiser.