Question

A geostationary satellite is orbiting the earth at a height 6R above the surface of the earth, where R is the radius of the earth. This time period of another satellite at a height (2.5 R) from the surface of the earth is ______.

विकल्प

• 10 hours

• `6sqrt2` hours

• `6sqrt3` hours

• 6 hours

Answer 1

A geostationary satellite is orbiting the earth at a height 6R above the surface of the earth, where R is the radius of the earth. This time period of another satellite at a height (2.5 R) from the surface of the earth is `underline(6sqrt2  "hours")`.

Explanation:

T² ∝ R³

`T_2/T_1=(R_2/R_1)^(3/2)=((3.5R)/(7R))^(3/2)=(1/2)^(3/2)=1/(2sqrt2)`

`T_2=1/(2sqrt2)  T_1=1/(2sqrt2)xx24  "hours"`

`T_2=6sqrt2  "hours"`