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A planet of mass $m$ moves in a circular orbit of radius $r$ with period $T$. The orbital speed of the planet is given by:
A$v = \dfrac{r}{2\pi T}$
B$v = \dfrac{\pi r^2}{T}$
C$v = \dfrac{2\pi r^2}{T}$
D$v = \dfrac{2\pi r}{T}$
Answer & Solution
Correct answer: D. $v = \dfrac{2\pi r}{T}$
1. Speed $= \dfrac{\text{distance travelled}}{\text{time taken}}$.
2. In one revolution the planet covers the perimeter of the orbit $= 2\pi r$.
3. The time taken for one revolution is the period $T$.
4. So $v = \dfrac{2\pi r}{T}$; options with $r^2$ confuse area with perimeter and are wrong.
_Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.14_
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