-->

Motion In Straight Line

Question
CBSEENPH11020682

The radii of circular orbits of two satellites A and B of the earth are 4R and R, respectively. If the speed of satellite A is 3v. then the speed of satellite B will be

  • 3v/4

  • 6v

  • 12 v

  • 3v/2

Solution

B.

6v

Orbital velocity of satellite
straight v space equals space square root of GM over straight r end root
fraction numerator straight v subscript straight A over denominator straight v subscript straight B space end fraction space equals space square root of straight r subscript straight B over straight r subscript straight A end root space equals space square root of fraction numerator straight R over denominator 4 straight R end fraction end root space equals 1 half

therefore comma space straight v subscript straight A over straight v subscript straight B space equals space fraction numerator 3 straight v over denominator straight v subscript straight B end fraction space equals space 1 half

therefore comma space straight v subscript straight B space equals space 6 straight v