For a satellite in an orbit around the earth, the ratio of kinetic energy to potential energy is:
For a satellite in an orbit around the earth, the ratio of kinetic energy to potential energy is:
- $\frac{1}{2}$
- $\frac{1}{\sqrt{2}}$
- 2
- $\sqrt{2}$
Solution
$-\frac{\mathrm{GMm}}{R^2}+m \omega^2 R=0$
$\begin{aligned}
\therefore \quad \frac{\mathrm{GMm}}{R^2} & =m \omega^2 R \\
\text { K.E. }=\frac{1}{2} I \omega^2 & =\frac{1}{2} m R^2 \omega^2 \\
& =\frac{\mathrm{GMm}}{2 R}
\end{aligned}$
$\begin{aligned}
& P . E .=-\frac{\mathrm{GMm}}{R} \therefore K . E=\frac{|P \cdot E|}{2} \\
& \therefore \quad \frac{K \cdot E}{P \cdot E}=\frac{1}{2}
\end{aligned}$
.
Asked in: NEET 2005
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