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Two satellites of masses m 1 and m 2 (m 1 =9m 2 ) are revolving around the earth in circular orbits of radii r and 9r. What is the ratio of the speeds of the satellites?

Two satellites of masses m1 and m2 (m1=9m2) are revolving around the earth in circular orbits of radii r and 9r. What is the ratio of the speeds of the satellites?

Grade:12th pass

1 Answers

Aafiya Shaikh
49 Points
3 years ago
We know that , centripetal force is F(c)=mv^2/r.Gravitational force is F(g)=GMm/r^2.Where,m=satellite massM=Earth massV=orbital velocityr=orbital radius G=gravitational constant...Since satellites are executing circular motion around Earth,so,equqting both forces,mv^2/r = GMm/r^2....,v^2=GM/r.....this is the relation between orbital radius and orbital velocity....Now for ratio of speed of satellites...v(1)^2/v(2)^2 = r(2)/r(1).....Here,,r(2)=9r,,,r(1)=r...now putting the value,,we get,,v(1)/v(2)=√9r/√r=3......So ratio of speed of satellites is 3:1..

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