Question

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 [CBSE AIPMT 2012]

Moderate

Solution

Force due to particle, $F = \frac{G M_{e} m}{R_{p}^{2}}$
Here, $F = \frac{G M_{p} m}{{(D_{p} / 2)}^{2}} \Rightarrow F = \frac{4 G M_{p} m}{D_{p}^{2}}$
Also, $F = m g$
$∴$ Acceleration due to gravity, $g = \frac{F}{m} = \frac{4 G M_{p}}{D_{p}^{2}}$

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