JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Gravitation

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Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :

(A)2 W
(B)W
(C) $2 W$
(D) $2^{\frac{1}{3}} W$ ✓ Correct

Answer: (D)

Solution

Surface gravity

g = \frac{4}{3} π R ρG

. Since density

ρ = \frac{M}{\frac{4}{3} π R ^{3}}

, we have

R \propto M^{1/3}

(for constant density). Thus

g \propto M^{1/3}

. For a planet with mass

2 M_{earth}

and same density,

g_{planet} = 2^{1/3} g_{earth}

. Therefore, weight

W^{'} = 2^{1/3} W

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option

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