NTA Abhyas JEE Main2020PhysicsGravitationPractice
Suppose the earth was covered by an ocean of uniform depth h. h ≪ R . let σ be density of ocean and ρ be mean density of earth. Let ∆ g be the approximate difference of value of net acceleration due to gravity between the bottom of the ocean and top Δ g = g t o p - g b o t t o m choose the correct option.
Options
- A∆ g = 4 3 π G h 2 ρ - 3 σ
- B∆ g = 4 3 G π h 3 σ - 2 ρ
- C∆ g = 4 3 G π h [ 2 σ - 3 ρ ]
- D∆ g = 4 3 G π h 3 ρ - 3 σ
Correct answer
B. ∆ g = 4 3 G π h 3 σ - 2 ρ
Step-by-step solution
g A = 4 3 G π R ρ g B =   G 4 3 π ρ R 3 + 4 3 π R + h 3 - 4 3 πR 3 σ R + h 2 ≈ 4 3 G π ρ R 1 - 2 h R + 4 3 G π R + h - 1 - 2 h R R σ ∆ g = g B - g A = 4 3 π G h 3 σ - 2 ρ