Gravitation

JEE Main level, single correct, medium

197 of 223

Question 197 of 223

A satellite of mass mm revolves around the earth of radius RR at a height xx from its surface. If gg is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

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Answer: (D) (gR2R+x)1/2\left(\frac{g R^2}{R+x}\right)^{1 / 2}

For the satellite, the gravitational force provides the necessary centripetal force i.e.
GMem(R+X)2=Mv02(R+X) and GMeR2=g∴v0=(gR2R+X)1/2\begin{aligned} & \frac{\mathrm{GM}_{\mathrm{e}} \mathrm{m}}{(\mathrm{R}+\mathrm{X})^2}=\frac{\mathrm{Mv}_0^2}{(\mathrm{R}+\mathrm{X})} \text { and } \frac{\mathrm{GM}_{\mathrm{e}}}{\mathrm{R}^2}=\mathrm{g} \\ & \therefore \mathrm{v}_0=\left(\frac{g \mathrm{R}^2}{\mathrm{R}+\mathrm{X}}\right)^{1 / 2} \\ & \end{aligned}

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