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If the radius of the earth be increased ...

If the radius of the earth be increased by a factor of `5`, by what factor its density be changed to keep the value of `g` of the same?

Text Solution

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`g = (GM)/(R^(2)) = (G)/(R^(2)) xx (4)/(3) pi R^(3) rho = (4)/(3) pi g R rho`
As per question , `g = (4)/(3) pi G R rho = (4)/(3) pi G(2R) rho'`
or `rho' = rho//2`
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Knowledge Check

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