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Question

An artificial satellite moves in a circular orbit around the earth. Total energy of the satellite is given by $$E$$. The potential energy of the satellite is:


A
2E
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B
2E
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C
2E3
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D
2E3
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Solution

The correct option is B $$2E$$
Let an artificial satellite of mass $$m$$ revolves around the earth in circular orbit of radius $$r$$.
The centrifugal force acting on the satellite is balanced by the gravitation due to earth.
$$\therefore   F_c  = F_G$$             $$\implies  \dfrac{mv^2}{r}  = \dfrac{GMm}{r^2}$$
$$mv^2  = \dfrac{GMm}{r}$$                             ............(1)
$$\therefore$$  Kinetic energy of the satellite        $$K.E  = \dfrac{1}{2}mv^2  = \dfrac{GMm}{2r}$$

Potential energy of the satellite         $$P.E =- \dfrac{GMm}{r}$$                       ...............(2)

Total energy of the satellite             $$E = K.E + P.E  = \dfrac{GMm}{2r}  - \dfrac{GMm}{r} $$
$$\implies  $$  $$E  = \dfrac{-GMm}{2r}$$                                  ..........(3)
From (2) and (3),  we get               $$P.E = 2E$$

Physics

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