Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r and 3r respectively. The ratio

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

Accepted Answer

Given: Two satellites move in circular orbits of radii $r$ and $3r$ . Their masses are $m$ and $3m$ , but orbital speed depends on the mass of Earth and the orbital radius, not on the satellite mass.

Find: The ratio of their orbital speeds.

For a satellite in circular orbit,

v = \sqrt{\frac{GM}{r}}

So,

v \propto \frac{1}{\sqrt{r}}

For orbital radii $r_1 = r$ and $r_2 = 3r$ ,

\frac{v_1}{v_2} = \sqrt{\frac{r_2}{r_1}}

Substituting,

\frac{v_1}{v_2} = \sqrt{\frac{3r}{r}} = \sqrt{3}

Therefore, the ratio of orbital speeds is $\sqrt{3}:1$ .

The solution working gives $\sqrt{3}:1$ , but the solution labels the correct option as A, which conflicts with the listed options. Based on the working, the defensible correct option is C.

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