Gravitation

JEE Main level, single correct, medium

175 of 223

Question 175 of 223

Two satellites of masses mm and 3m3m revolve around the earth in circular orbits of radii r&3r respectively. The ratio of orbital speeds of the satellites respectively is

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Answer: (A) 3:1\sqrt{3}:1

The orbital velocity is given
V=(GMr)V=\sqrt{\left(\dfrac{GM}{r}\right)}
where MM is the mass of earth and rr is the radius of the orbit of satellite.
The velocity of the satellite with mass mm is
V1=GMr{V}_{1}=\sqrt{\dfrac{GM}{r}}
and the velocity of the satellite with mass 3m3m is
V2=GM3r{V}_{2}=\sqrt{\dfrac{GM}{3r}}
Hence, the ratio of the velocities is
V1V2=3rr=31\dfrac{{V}_{1}}{{V}_{2}}=\sqrt{\dfrac{3r}{r}}=\dfrac{\sqrt{3}}{1}

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