# A spherical planet far out in space has a mass M0 and diameter D0. A particle of mass m falling freely near the surface of this planet will experience an acceleration due to gravity which is equal to Option 1) $\frac{GM_{0}}{D^{2}_{0}}$ Option 2) $\frac{4mGM_{0}}{D^{2}_{0}}$ Option 3) $\frac{4GM_{0}}{D^{2}_{0}}$ Option 4) $\frac{GmM_{0}}{D^{2}_{0}}$

As we learnt in

Acceleration due to gravity (g) -

Force extended by earth on a body is gravity.

Formula:    $g=\frac{GM}{R^{2}},$

$g=\frac{4}{3}\pi \rho \, GR$

$g\rightarrow$ gravity

$\rho \rightarrow$ density of earth

$R \rightarrow$ Radius of earth

- wherein

It's average value is $9.8\: m/s^{2}\; \; or \; \; 981cm/sec^{2}\; or\; 32feet/s^{2}$ on the surface of earth

Acceleration due to gravity$=\frac{GM_{o}}{R_{o}^{2}}=\frac{GM_{o}}{\left ( \frac{D_{o}}{2} \right )^{2}}=\frac{4GM_{o}}{D_{o}^{2}}$

Option 1)

$\frac{GM_{0}}{D^{2}_{0}}$

This is incorrect option

Option 2)

$\frac{4mGM_{0}}{D^{2}_{0}}$

This is incorrect option

Option 3)

$\frac{4GM_{0}}{D^{2}_{0}}$

This is correct option

Option 4)

$\frac{GmM_{0}}{D^{2}_{0}}$

This is incorrect option

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