The density of the core of planet is ρ 1 and that of the outer shell is ρ 2 . The radius of the core and that of the planet are R and 2R respectively. Gravitational intensity at the surface of the

Question

The density of the core of planet is ρ 1 ​ and that of the outer shell is ρ 2 ​ . The radius of the core and that of the planet are R and 2R respectively. Gravitational intensity at the surface of the planet is same as at a depth R. Find the ratio ρ 2 ​ 3 ρ 1 ​ ​ , assuming them to be uniform independently.

TestHub · Accepted Answer

At depth R only the core attracts: g d ​ = R 2 G ρ 1 ​ 3 4 ​ π R 3 ​ = 3 4 π G ρ 1 ​ R ​ . At the surface: g s ​ = ( 2 R ) 2 G 3 4 ​ π R 3 ( ρ 1 ​ + 7 ρ 2 ​ ) ​ = 3 π GR ( ρ 1 ​ + 7 ρ 2 ​ ) ​ . Equating: 4 ρ 1 ​ = ρ 1 ​ + 7 ρ 2 ​ , so ρ 2 ​ 3 ρ 1 ​ ​ = 7 .

Physics - Gravitation Question with Solution | TestHub

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