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  4. Two satellites of masses 3 M and M orbit the earth in circular orbits of radii r and 3 r respectively. The ratio of their speeds is

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Q. Two satellites of masses $3\, M$ and $M$ orbit the earth in circular orbits of radii $r$ and $3\, r$ respectively. The ratio of their speeds is

Bihar CECEBihar CECE 2009Work, Energy and Power

Solution:

Orbital velocity $v=\sqrt{\frac{G M}{r}}$.
where, $M =$ mass of the planet
$r=$ radius of the orbit
Orbital velocity is independent of the mass of the orbiting body and is always along the tangent of the orbit. For a given planet (here earth), greater the radius of orbital, lesser will be the orbital velocity of the satellite
$\left(v \propto \frac{1}{\sqrt{r}}\right)$
$\therefore \frac{v_{1}}{v_{2}}=\sqrt{\frac{r_{2}}{r_{1}}}=\sqrt{\frac{3}{1}}$