First slide

Concept of potential energy

Question

A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to $- K / r^{2}$ , where K is a constant. The total energy of the particle is

Moderate

A

$\frac{K}{2 r}$
B

$- \frac{K}{2 r}$
C

$- \frac{K}{r}$
D

$\frac{K}{r}$

Solution

Here $\frac{{mv}^{2}}{r} = \frac{K}{r^{2}} ∴$ K.E. $= \frac{1}{2} {mv}^{2} = \frac{K}{2 r}$
$U = - \int_{\infty}^{r} F . dr = - \int_{\infty}^{r} (- \frac{K}{r^{2}}) dr = - \frac{K}{r}$
Total energy $E = K.E. + P.E. = \frac{K}{2 r} - \frac{K}{r} = - \frac{K}{2 r}$

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