Physics

Problem

![](https://storage.googleapis.com/diraq-contents/question-bank/question-images/92101d51834e/2025_11_20_928013a02c702487609fg-04.jpg) 18. The figure above represents satellites

\mathrm{S}_{2}

and

\mathrm{S}_{3}

of equal mass orbiting Earth in circles of radii

2 R_{e}

and

3 R_{e}

, respectively, where

R_{e}

is the radius of Earth. How do the kinetic energy and the angular momentum of

\mathrm{S}_{3}

compare with those of

\mathrm{S}_{2}

? Kinetic Energy (A) Less for

\mathrm{S}_{3}

(B) Greater for

\mathrm{S}_{3}

\mathrm{S}_{3}

(E) Greater for

\mathrm{S}_{3}

Angular Momentum Greater for

\mathrm{S}_{3}

Greater for

\mathrm{S}_{3}

The same for both Less for

\mathrm{S}_{3}

Less for

\mathrm{S}_{3}

Intuitive explanation

The key is recognizing that orbital speed and angular momentum both depend on orbital radius through gravitational force balance. For circular orbits, gravity provides centripetal force, which gives you $v \propto 1/\sqrt{r}$ —so satellites farther out move slower, reducing kinetic energy. However, angular momentum $L = mvr$ combines both the slower speed and the larger radius; the radius effect dominates, making $L$ increase with orbital distance. Compare the two satellites by finding how each quantity scales with $r$ .

Intuitive explanation

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