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}}

 

Answers (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)

\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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