Question

A body of mass $2kg$ is moving under the influence of a central force whose potential energy is given by $U=2r^{3}J$ If the body is moving in a circular orbit of $5m$ its energy will be

• A. $625J$
• B. $250J$
• C. $500J$
• D. $125J$

Answer 1

The correct option is A $625J$

$F=-\frac{dU}{dr}$

$F=-6r^2$

This force must be equal to centripetal force:

$F=\frac{m{v}^2}{r}=6r^2$

kinetic energy $=\frac{1}{2}m{v}^2=3r^3$

total mechanical energy:

$M.E.=3r^3+2r^3=5r^3$

$M.E.=625J$