When we draw the variation of the potential energy of a pair of nucle…

The correct answer is Option (1) → the force is attractive when separation between them is greater than 0.8 fm

The nuclear force between two nucleons is read from the slope of their potential energy curve, \( F = -dU/dr \). The curve has its minimum at about \( r_0 = 0.8\,\mathrm{fm} \).

For \( r \gt r_0 \) the potential energy rises as the nucleons move apart, so the force pulls them together: it is attractive. For \( r \lt r_0 \) the potential energy rises steeply as they come closer, so the force pushes them apart: it is strongly repulsive.

Option (1) the force is attractive when separation between them is greater than 0.8 fm — Correct. Above about 0.8 fm the force is attractive.

Option (2) the force is repulsive when separation between them is greater than 0.8 fm — Incorrect. Above 0.8 fm the force is attractive; repulsion appears only below 0.8 fm.

Option (3) the force is attractive when separation between them is less than 0.8 fm — Incorrect. Below 0.8 fm the force is repulsive.

Option (4) the force is independent of their separation — Incorrect. The force changes from repulsive to attractive and then vanishes as the separation grows, so it depends strongly on the separation.

NCERT (2026-27):
Nuclear Force – “… A rough plot of the potential energy between two nucleons as a function of distance is shown in the Fig. 13.2. The potential energy is a minimum at a distance r₀ of about 0.8 fm. This means that the force is attractive for distances larger than 0.8 fm and repulsive if they are separated by distances less than 0.8 fm.”