Figure shows the variation of the gravitatioal acceleration a g of four planets with the radial distance r from the centre of the planet for r ≥ radius of the planet. Plots 1 and 2 coincide for r ≥

Question

Figure shows the variation of the gravitatioal acceleration $a_{g}$ of four planets with the radial distance r from the centre of the planet for $r \geq$ radius of the planet. Plots 1 and 2 coincide for $r \geq R_{2}$ and plots 3 and 4 coincide for $r \geq R_{4}$ . The sequence of the planets in the descending order of their densities is :

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Outside a planet a g = r 2 GM . Plots 1 and 2 coincide for r ≥ R 2 , so M 1 = M 2 ; with R 1 < R 2 , density ρ 1 > ρ 2 . Similarly plots 3 and 4 coincide for r ≥ R 4 , so M 3 = M 4 ; with R 3 < R 4 , ρ 3 > ρ 4 . At r = R 2 = R 3 the 1,2 curve lies above the 3 curve, so M 1 > M 3 ; since R 2 = R 3 this gives ρ 2 > ρ 3 . Hence ρ 1 > ρ 2 > ρ 3 > ρ 4 .

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