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Energy required to move a body of mass  from  an orbit of radius  2R  to  3R  is

  • Option 1)

    GMm/12 R^{2}

  • Option 2)

    GMm/3 R^{2}

  • Option 3)

    GMm/8 R

  • Option 4)

    GMm/6 R


Answers (1)


As we learnt in 

Work done in changing the orbit -


W=\frac{GMm}{2}\left [ \frac{1}{r_{1}}-\frac{1}{r_{2}} \right ]

W\rightarrow work\: done

r_{1}\rightarrow radius\: of\: 1st\: orbit

r_{2}\rightarrow radius\: of\: 2nd\: orbit

- wherein

When satellite is transferred to higher orbit 

\left ( r_{2}>r_{1} \right )

Use given equation


 E = \dpi{100} (P.E)_{3R}-(P.E)_{2R}

=-\frac{GmM}{3R}-\left ( -\frac{GmM}{2R} \right )=+\frac{GmM}{6R}

Option 1)

GMm/12 R^{2}

This option is incorrect.

Option 2)

GMm/3 R^{2}

This option is incorrect.

Option 3)

GMm/8 R

This option is incorrect.

Option 4)

GMm/6 R

This option is correct.

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