Question

A geostationary satellite is orbiting the earth at a height of 6R above the surface of the earth, where R is the radius of the earth. The time period of another satellite at a height of 2.5 R from the surface of the earth is …… hours.
A. `6sqrt2` hours
B. `6sqrt(2.5)` hours
C. `6sqrt3` hours
D. 12 hourse.

Answer 1

Correct Answer - a
`(T_(1))/(T_(2))=((r_(1))/(r_(2)))^(3//2)" or "T_(2)=T_(1)((r_(2))/(r_(1)))^(3//2)`
`T_(1)="1 day = 24 hours and "r_(1)=6R+R=7R.`
`r_(2)=2.5R+R=3.5R.`
`therefore" "T_(2)=24xx((3.5R)/(7R))^(3//2)=24xx((1)/(2))^(3//2)=6sqrt2" hrs"`