Question

Potential energy v/s position graph is as shown in
the figure. The corresponding force-position
graph is best represented by
​

Answer 1

relation between potential energy and force is given as, F = - dU/dx

i.e., force is the negative of rate of change of potential energy with respect to position.

now let's start to plot force - position graph.

case 1 : 0 < x < x1

potential energy is directly proportional to its position.

⇒U ∝ x

⇒ U = kx , where k is proportionality constant.

so force , F = -dU/dx = -d(kx)/dx = -k

so, graph of force - position is a straight parallel to x-axis between 0 to x1.

case 2 : x1 < x < x2

potential energy doesn't depend on position.

so, U = constant (C)

then, force = - dU/dx = -d(C)/dx = 0

hence, force - position graph doesn't exist between x1 to x2 .