Question

A spherical planet has mass M and diameter D. A particle of mass mp is falling near the surface of planet. Due to the falling particle, planet will experience an acceleration equal to

Answer 1

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)

This is correct option

Option 4)

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

This is incorrect option