AIIMS 2019 Physics Acceleration due to gravity MCQ Question
A planet has same density as that of earth and universal gravitational constant is twice that of earth, the ratio of acceleration due to gravity, is.
1:4
1:5
1:2
3:2
Correct Answer
Detailed Explanation
To find the acceleration due to gravity at the surface of a planet with density ρₚ and gravitational constant Gₚ, we substitute M = (4/3)πRₚ³ρₚ into the equation g = GM/R². Given that ρₑ = ρₚ and Gₚ = 2Gₑ, we can express gₚ as gₚ = (Gₚ(4/3)πRₚ³ρₚ) / Rₚ², which simplifies to Gₚ(4πRₚ³/3)ρₚ/Rₚ². This shows that option C correctly represents the relationship for gravity on planet P.
Options A and B are incorrect because they do not account for the specified relationships between the densities and gravitational constants, while option D does not include the necessary mass and density terms in the context of gravity calculations.
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