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Imagine a new planet having the same den...

Imagine a new planet having the same density as that of earth but `3` times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is `g` and that on the new plane is `g` , then :

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The correct Answer is:
3
Given `R'=3R, M=4/3piR^(3)rho`
`g'=GMR^('2)`
putting `M'=4/3piR^('3)rho`
`g'=G/R^('2)4/3piR^('3)rho=27/9 G/(R^(2)) 4/3R^(3)rho=3(GM)/(R^(2))=3g`
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