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Question

# A planet's density is 3 times that of the Earth. But the acceleration due to gravity on its surface is exactly the same as on the Earth's surface. The radius of the planet in terms of the Earth's radius R is

A
2R
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B
3R
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C
R3
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D
none of the above
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Solution

## The correct option is C R3In general we know that, force of gravity between two objects (M and m) at a distance r is given by: F=GMmr2 Also F=mg∴g=GMr2Now, acceleration due to gravity on the planet's surface is exactly the same as on the Earth's surface: gp=geGMpr2p=GMer2eMpr2p=Mer2e - (1)Given: ρp=3×ρe4/3πr3pr2p×3=4/3πr3er2e∴3rp=rerp=R3

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