The potential energy of a particle on the line y = 2 x are same at every point. The conservative force on a the particle at (1,2) may be

Sol: As Potential Energy decreases in the direction of force and remains constant in the perpendicular direction of force .

$F = -\frac{dU}{dr}$

Slope in the direction of line = 2 and slope in perpendicular direction = -1/2 since m₁ × m₁ = -1

hence , $\vec{F} = – 8 \hat{i} + 4 \hat{j}$ ; because slope = 4/-8 = -1/2