Gravity on a new planet with same density – Rankers Physics

Acceleration Due to Gravity and its variation: Practice Problem & Solution

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: (2005)
$g' = 3g$
$g' = \frac{g}{9}$
$g' = 9g$
$g' = \frac{g}{3}$

Solution Explained:

To solve this problem, we apply the core principles of Acceleration Due to Gravity and its variation. Understanding the underlying formula is key to arriving at the correct answer below:

Acceleration due to gravity in terms of density is $g = \frac{4}{3}\pi \rho G R$. Since density $\rho$ is constant, $g \propto R$. For a planet $3$ times bigger in size ($R' = 3R$), the new gravity is $g' = 3g$.

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