The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is 9:4. The mass of the planet is \frac{1}{9}th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet?(Take the planets to have the same mass density)

 

  • Option 1)

    \frac{R}{3}

     

     

     

  • Option 2)

    \frac{R}{4}

  • Option 3)

    \frac{R}{9}

  • Option 4)

    \frac{R}{2}

 

Answers (1)

 

Newton's Law of Gravitation -

F\; \alpha\; \frac{m_{1}m_{2}}{r^{2}}

F\; = \frac{G\, m_{1}\, m_{2}}{r^{2}}

F\rightarrow Force    

G\rightarrow Gravitalional constant

m_1,m_2\rightarrow  Masses

r\rightarrow  Distance between masses

- wherein

Force is along the line joining the two masses

 

 

1 - planet                 2- Earth

W_{1}=\frac{GM_{1}m}{R^{2}_{1}}            W_{2}=\frac{GM_{2}m}{R^{2}_{2}}

\frac{W_{1}}{W_{2}}=\frac{M_{1}}{M_{2}}\left ( \frac{R_{2}^{2}}{R_{1}^{2}} \right )

\frac{4}{9}=\frac{1}{9}\left ( \frac{R_{2}^{2}}{R_{1}^{2}} \right )=\frac{R_{1}}{R_{2}}=\frac{1}{2}

Rplanet = \frac{Rearth}{2}


Option 1)

\frac{R}{3}

 

 

 

Option 2)

\frac{R}{4}

Option 3)

\frac{R}{9}

Option 4)

\frac{R}{2}

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