First slide

Concept of potential energy

Question

A conservative force is given by the function $F = \frac{K}{r^{2}}$ , K is a constant. If potential energy is zero at $r = r_{0}$ , then potential energy at $r = \infty$ is

Moderate

A

$\frac{k}{r_{0}}$
B

$\frac{k}{2 r_{0}}$
C

$\frac{- k}{r_{0}}$
D

$\frac{- k}{2 r_{0}}$

Solution

$\begin{array}{l} \int d U = - \int \vec{F} \cdot \vec{d r} \Rightarrow \int_{0}^{U} d U = - \int_{0}^{\infty} \frac{k}{r^{2}} \\ [U]_{0}^{U_{\infty}} = - K {[\frac{- 1}{r}]}_{r_{0}}^{\infty} \Rightarrow U_{\infty} - 0 = K [\frac{- 1}{\infty} + \frac{1}{r_{0}}] \\ U_{\infty} = \frac{- K}{r_{0}} \end{array}$

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