SATHEE: Gravitation Question 15

Gravitation Question 15

Question:The radii of two planets are respectively $[R_{1}]$ and $[R_{2}]$ and their densities are respectively $[ρ_{1}]$ and $[ρ_{2}]$ . The ratio of the accelerations due to gravity at their surfaces is [MP PET 1994]

Options:

A) $[g_{1} : g_{2} = \frac{ρ_{1}}{R_{1}^{2}} : \frac{ρ_{2}}{R_{2}^{2}}]$

B) $[g_{1} : g_{2} = R_{1} R_{2} : ρ_{1} ρ_{2}]$

C) $[g_{1} : g_{2} = R_{1} ρ_{2} : R_{2} ρ_{1}]$

D) $[g_{1} : g_{2} = R_{1} ρ_{1} : R_{2} ρ_{2}]$

Show Answer

Answer:

Correct Answer: D

Solution:

$[g = \frac{4}{3} π ρ G R]$ $[∴]$

$[\frac{g_{1}}{g_{2}} = \frac{R_{1} ρ_{1}}{R_{2} ρ_{2}}]$

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Gravitation Question 15

Question:The radii of two planets are respectively [R1] and [R2] and their densities are respectively [ρ1] and [ρ2] . The ratio of the accelerations due to gravity at their surfaces is [MP PET 1994]

Options:

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Question:The radii of two planets are respectively $[R_{1}]$ and $[R_{2}]$ and their densities are respectively $[ρ_{1}]$ and $[ρ_{2}]$ . The ratio of the accelerations due to gravity at their surfaces is [MP PET 1994]