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The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is 9: 4. The mass of the planet is 1/9 th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet? (Take the planets to have the same mass density)

1. R/9
2. R/2
3. R/3
4. R/4

Correct answer: R/2

Solution

Weight ratio gE/gP = (Me/Mp)*(Rp/Re)^2 = 9*(Rp/Re)^2 = 9/4, so (Rp/Re)^2 = 1/4 and Rp = R/2.

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