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A satellite is revolving in a circular orbit at a height h from the earth surface, such that h<<R where R is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is:

 

  • Option 1)

     

    \sqrt{gR}

  • Option 2)

     

    \sqrt{\frac{gR}{2}}

  • Option 3)

     

    \sqrt{2gR}

  • Option 4)

     

    \sqrt{gR}\left ( \sqrt{2}-1 \right )

Answers (1)

best_answer

 

Escape velocity ( in terms of radius of planet) -

V_{c}=\sqrt{\frac{2GM}{R}}

V_{c}=\sqrt{2gR}

V_{c}\rightarrow Escape velocity

R\rightarrowRadius of earth

- wherein

  • depends on the reference body
  • greater the value of \frac{M}{R} or \left ( gR \right ) greater will be the escape velocity V_{e}=11.2Km/s  For earth

 

V_{o}=\sqrt{g(R+h)}

\approx \sqrt{gR}

V_{e}=\sqrt{2g(R+h)}\approx \sqrt{2gR}

\Delta V=V_{e}-V_{o}=(\sqrt{2-1})\sqrt{gR}


Option 1)

 

\sqrt{gR}

Option 2)

 

\sqrt{\frac{gR}{2}}

Option 3)

 

\sqrt{2gR}

Option 4)

 

\sqrt{gR}\left ( \sqrt{2}-1 \right )

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