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Q.

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

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a

$\frac{{GM}_{p} m}{{D_{p}}^{2}}$

b

$\frac{{GM}_{p}}{{D_{p}}^{2}}$

c

$\frac{4 {GM}_{p} m}{{D_{p}}^{2}}$

d

$\frac{4 {GM}_{p}}{{D_{p}}^{2}}$

answer is B.

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Detailed Solution

detailed_solution_thumbnail

Force, F = $\frac{{GM}_{e} m}{R^{2}}$

Here, F = $\frac{{GM}_{p} m}{{(\frac{D_{p}}{2})}^{2}} = \frac{4 {GM}_{p} m}{{D_{p}}^{2}}$

We know F = ma

Acceleration due to gravity a = $\frac{F}{m} = \frac{4 {GM}_{p}}{{D_{p}}^{2}}$

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