JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Gravitation

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A planet has double the mass of the earth. Its average density is equal to the that of the earth. An object weighing W on earth will weigh on that planet :

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

Answer: (C)

Solution

Since the planet has the same density as Earth but double the mass:

m = ρ \times \frac{4}{3} π R^{3}

With constant density,

R \propto m^{1/3}

. So if mass doubles,

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

.

Weight

W = m g

, where

g = \frac{GM}{R ^{2}}

. Therefore:

W \propto \frac{m}{R ^{2}} = \frac{m}{m ^{2/3}} = m^{1/3}

Since the planet's mass is twice Earth's:

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

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Single correct option

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