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  4. Imagine a new planet having the same density as that of earth but it is 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 surface of the new planet is g', then

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

AIPMTAIPMT 2005Gravitation

Solution:

$ g= \frac{ GM}{r^2 } $ and $ g' = \frac{ GM' }{r^2} [ M' = 3M ] $
$ \frac{g'}{ g } = \frac{ 3M}{M} $
$\Rightarrow g' =3g $.