Acceleration due to gravity on a spherical planet – Rankers Physics

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

A spherical planet has a mass $M_P$ and diameter $D_P$. A particle of mass $m$ falling freely near the surface of this planet will experience an acceleration due to gravity, equal to: (2012 Pre)
$\frac{4GM_P}{D_P^2}$
$\frac{GM_Pm}{D_P^2}$
$\frac{GM_P}{D_P^2}$
$\frac{4GM_Pm}{D_P^2}$

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 is given by $g = \frac{GM_P}{R_P^2}$. Substituting the radius as half of the diameter, $R_P = \frac{D_P}{2}$, we get $g = \frac{GM_P}{(D_P/2)^2} = \frac{4GM_P}{D_P^2}$.

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