The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is '…

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is ' $\mathrm{V}$ '. For the satellite orbiting at an altitude of half the earth's radius, the orbital velocity is
  1. $\frac{3}{2} \mathrm{~V}$
  2. $\sqrt{\frac{3}{2}} \mathrm{~V}$
  3. $\sqrt{\frac{2}{3}} \mathrm{~V}$
  4. $\frac{2}{3} \mathrm{~V}$

Solution

The orbital velocity near the surface of the earth $\mathrm{V}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}$ At an altitude $\frac{R}{2}$, the orbital velocity $V^{\prime}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}+\frac{\mathrm{R}}{2}}}=\sqrt{\frac{2 \mathrm{GM}}{3 \mathrm{R}}}=\sqrt{\frac{2}{3}} \mathrm{~V}$

Asked in: MHT CET 2021 (20 Sep Shift 2)

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