1.

The mean radius of earth is R and its angular speed about its own axis is omega and accelerationdue to gravity is 'g'. The cube of the radius of the orbit of geostationary satellite is :

Answer»

`(R^(2)g)/(omega)`
`(R^(2)omega^(2))/(g)`
`(Rg)/(omega^(2))`
`(R^(2)g)/(omega^(2))`

Solution :Here time period of a satellite is
`T=2PI sqrt((r^(3))/(GM))`
`therefore (T)/(2pi)=sqrt((r^(3))/(GM)) or (1)/(omega)=sqrt((r^(3))/(GR^(2)))`
`(1)/(omega^(2)) = (r^(3))/(gR^(2)) or r^(3)=(gR^(2))/(omega^(2))`.
Correct choice is (d).


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