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Question

Consider a planet in some system which has a mass double the mass of the earth and density equal to the average density of the earth. If an object weighs W on the earth, then its weight on the planet is:

A
W
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B
2W
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C
W2
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D
21/3W
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Solution

The correct option is D 21/3W
Answer is D.

Let m be the mass of the body. Let W be the weight of the body on the earth.
W = mg.
G=GMR2 (for the earth).
Mass of the planet =2× (Mass of the earth)
That is, M=2M.
43πR3ρ=2×43πR3ρ.
R=(2)13×R.
So, W=(2)13×W.
Hence, If an object weights W on the earth then its weight on the planet is (2)13×W.

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