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A geostationary satellite is orbiting th...

A geostationary satellite is orbiting the earth at a height of `5R` above the surface of the earth, `2R` being the radius of the earth. The time period of another satellite in hours at a height of `2R` form the surface of the earth is

A

`10`

B

`13`

C

`8sqrt(3)`

D

`8sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
As `T^(2) prop r^(3)`,
`:. (T_(1)^(2))/(T_(2)^(2)) = ((5R + R)^(3))/((3R + R)^(3)) = ((6R)/(4R))^(3)`
`T_(2) = T_(1) ((3R + R)/(5R + R))^(3//2) = T_(1) ((4)/(6))^(3//2) = T_(1) ((2)/(3))^(3//2)`
`= 24 xx (2sqrt(2))/(3sqrt(3)) = (8xx2xx sqrt(2) xx sqrt(3))/(3)`
`= (16)/(3) sqrt(6) = (16)/(3) xx 2.45 = 13 h`
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