JEE Main · 2023 · 08 Apr 2023 · Shift 1 · Gravitation

For a satellite of mass $m$ in a circular orbit of radius $r$, the kinetic energy is $K=\frac{GMm}{2r}$, the potential energy is $U=-\frac{GMm}{r}$, and the total energy is $E=K+U=-\frac{GMm}{2r}$. Comparing these gives $U=2E$ and $K=-E=|E|$. Statement I claims the potential energy equals $\frac{E}{2}$, whereas it is $2E$, so Statement I is incorrect. Statement II claims the kinetic energy equals half the magnitude of the total energy, whereas it equals the full magnitude $|E|$, so Statement II is incorrect. Hence both statements are incorrect.