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
B
2E
C
2E3
D
2E3

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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