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(D) For a satellite of mass $m$ to revolve in a circular orbit of radius $r$ around a planet of mass $M$,the gravitational force provides the necessar

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$v^2 = \frac{GM}{r}$

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(D) For a satellite of mass $m$ to revolve in a circular orbit of radius $r$ around a planet of mass $M$,the gravitational force provides the necessary centripetal force.The gravitational force is given by $F_g = \frac{GMm}{r^2}$.The centripetal force required for circular motion is $F_c = \frac{mv^2}{r}$.Equating the two forces:$\frac{mv^2}{r} = \frac{GMm}{r^2}$.Canceling $m$ from both sides and multiplying by $r$:$v^2 = \frac{GM}{r}$.Thus,the correct expression is $v^2 = \frac{GM}{r}$.

If $r$ represents the radius of the orbit of a satellite of mass $m$ moving around a planet of mass $M$,the velocity of the satellite is given by

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