First slide

Conservative force a negative gradient of potential energy

Question

A particle can move along x-axis under the influence of a conservative force and variation of its potential energy is as shown in the figure. Then

Moderate

A

force acting on the particle is zero at $x = x_{1}$ and $x_{3}$
B

force acting on the particle at $x = x_{1}$ , points in the right.
C

force acting on the particle at $x = x_{3}$ , points in the right
D

force acting on the particle at $x = x_{2}$ , points in the left.

Solution

$F = - \frac{d U}{d x} =$ negative of the slope of tangent. Now $\frac{d U}{d x}$ is negative at $x = x_{1}$ , so F is positive i.e directed to the right. $\frac{d U}{d x}$ is positive at $x = x_{3}, \frac{d U}{d x} = 0$ , so the force is zero.

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