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Question

# Two artificial satellites of masses 'm' and '6m' orbit the earth in circular orbits of radii 'r' and '4r' respectively. The ratio of their orbital speeds is:

A

12
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B

4
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C
2
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D
2
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Solution

## The correct option is D 2Given, Mass of 1st satellite (m1) = m Mass of 2nd satellite (m2)= 6m Radius of orbit of 1st satellite (r1) = r Radius of orbit of 2nd satellite (r2)= 4r The orbital speed of a satellite: v=√GMr where, r is the orbital radius of a satellite and M is the mass of the earth. As we can see, orbital velocity is independent of the mass of the satellite. So, Orbital velocity of 1st satellite: v1=√GMr1 Orbital velocity of 2nd satellite: v2=√GMr2 Therefore, the ratio of orbital velocities of 1st satellite to 2nd satellite: v1v2=√r2r1 =√4rr =√4 =2 Hence, the required ratio is 2

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