# A satellite of mass  m revolves around the earth of  radius R  at a height  x  from its surface .If    g   is the  acceleration due to gravity on the surface of the  earth, the orbital speed of the satellite is Option 1) Option 2) Option 3) Option 4)

As we learnt in

For a satellite

centripetal force = Gravitational force

$\dpi{100} \therefore \; \; \frac{mv_{0}^{2}}{(R+x)}=\frac{GMm}{(R+x)^{2}}$

$\dpi{100} or\; \; \; v_{0}^{2}=\frac{GM}{(R+x)}=\frac{gR^{2}}{(R+x)}\; \; \; \; \; \; \; \left [ \because \; \; g=\frac{GM}{R^{2}} \right ]$

$\dpi{100} or\; \; \; v_{0}=\sqrt{\frac{gR^{2}}{R+x}}$

Orbital velocity of satellite -

Position of satellite from the centre of earth

Orbital velocity

- wherein

The velocity required to put the satellite into its orbit around the earth.

Option 1)

Incorrect

Option 2)

Incorrect

Option 3)

Incorrect

Option 4)

Correct

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