Gravitation

JEE Main level, single correct, medium

81 of 223

Question 81 of 223

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

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Answer: (C) 213W{2}^{\dfrac{1}{3}}W

Density is same
M=43πR3ρ,2m=43πR′3ρM=\dfrac{4}{3}\pi {R}^{3}\rho ,2m=\dfrac{4}{3}\pi {R}^{'3}\rho
R′=213R{R}^{'}={2}^{\dfrac{1}{3}}R
W=GMmR2W=\dfrac{GMm}{{R}^{2}}
W2=G2MmR′2{W}_{2}=\dfrac{G2Mm}{{R}^{'2}}
W2=213W{W}_{2}={2}^{\dfrac{1}{3}}W

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