Question

In a satellite if the time of revolution is T, then kinetic energy is proportional to.

• A. $\frac{1}{T}$
• B. $\frac{1}{T^2}$
• C. $T^{\frac{-3}{2}}$
• D. $T^{\frac{-2}{3}}$

Answer 1

The correct option is D $T^{\frac{-2}{3}}$

Time period T $\propto r^{\frac{3}{2}}\Rightarrow r\propto T^{\frac{2}{3}}$
And kinetic energy $\propto \frac{1}{r}\propto \frac{1}{T^{\frac{2}{3}}}\propto T^{-\frac{2}{3}}$