There will be a decrease in the potential energy of the system if work is done upon the system by:

Prove $F = - \frac{dV}{dx}$ for a conservative force.

When a conservative force does positive work on a body,

The potential energy $U$ between two molecules as a function of distance $x$ between them is shown. $A, B, C$ are points for which $x = 0.6 \mathring{A}, 1.2 \mathring{A}, 1.8 \mathring{A}$ respectively. At $A, B, C$,the force between the two molecules is:

The force acting on a body moving along the $x-$axis varies with the position of the particle as shown in the figure. The body is in stable equilibrium at

If $F = 2x^2 - 3x - 2$,then choose the correct option.