Question

A particle of mass m is moving in a horizontal circle of radius r with a centripetal force $F=-\frac{k}{r^2}\hat{r},$ where k = 1 unit. The total energy of the particle is

• A. $-\frac{k}{r}$
• B. $-\frac{1.5k}{r}$
• C. $-\frac{k}{2r}$
• D. $-\frac{3k}{2r}$

Answer 1

The correct option is C $-\frac{k}{2r}$

$f=-\frac{k}{r^2}=\frac{m{v}^2}{r}\Rightarrow KE=\frac{1}{2}m{v}^2=\frac{k}{2r}$
And potential energy $=-\int Fdr=-\int \frac{-k}{r^2}dr=[-\frac{k}{r}]$