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

$1$

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$\sqrt{3}$

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$\frac{1}{2 \sqrt{3}}$

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$\frac{1}{3}$

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Solution

The correct option is B
$\sqrt{3}$

The orbital speed of a satellite is given by $v = \sqrt{\frac{G M}{r}}$ where r is the orbital radius and M is the mass of the earth.
As we can see, orbital velocity is independent of the mass of the satellite.
$∴ \frac{v_{1}}{v_{2}} = \sqrt{\frac{r_{2}}{r_{1}}} = \sqrt{\frac{3 r}{r}} = \sqrt{3}$
Hence, the correct choice is (b).

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

The correct option is B √3 The orbital speed of a satellite is given by v=√GMr where r is the orbital radius and M is the mass of the earth. As we can see, orbital velocity is independent of the mass of the satellite. ∴v1v2=√r2r1=√3rr=√3 Hence, the correct choice is (b).