Question

A particle of mass m is moving in a circular path of radius r under the influence of centripetal force $F=\frac{-C}{r^2}$. The total energy of the particle is

• A. $-\frac{C}{2r}$
• B. $\frac{C}{2r}$
• C. $C\times 2r$
• D. $Zero$

Answer 1

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

F centripetal $F=\frac{m{v}^2}{r}=\frac{C}{r^2};U=-{\int }_{\alpha }Fdr=C\int r^{-2}dr=\frac{-C}{r};\therefore E_1=E_k+U=\frac{C}{2r}-\frac{C}{r}=-\frac{C}{2r}$