Given below are two statements :
Statement I : A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II : The time period of revolution of the satellite is T = 2π√(Rₑ/g) (for satellite very close to the earth surface), where Rₑ radius of earth and g acceleration due to gravity.
In the light of the above statements, choose the correct answer from the options given below :

Question

Given below are two statements :

Statement I : A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.

Statement II : The time period of revolution of the satellite is T = 2π√(Rₑ/g) (for satellite very close to the earth surface), where Rₑ radius of earth and g acceleration due to gravity.

In the light of the above statements, choose the correct answer from the options given below :

G1 Physics · Accepted Answer

For a satellite in a circular orbit very close to the Earth's surface, T = 2π√(Rₑ³/GMₑ). The Earth's mass is Mₑ = (4/3)πRₑ³ρ. Therefore, T = 2π√[Rₑ³/{G(4/3)πRₑ³ρ}]. The factor Rₑ³ cancels, so T ∝ 1/√ρ. Thus the period depends on the density of Earth. Statement I is true. Also, at the Earth's surface, g = GMₑ/Rₑ². Hence, GMₑ = gRₑ². Substitute this into T = 2π√(Rₑ³/GMₑ): T = 2π√(Rₑ³/{gRₑ²}) = 2π√(Rₑ/g). Therefore Statement II is also true. Correct option: B.