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MHT CET 2021 (20 Sep, Shift 1) · Satellites - Orbital Velocity & Period

Satellites - Orbital Velocity & Period question from MHT CET 2021 (20 Sep, Shift 1)

Q46MHT CET 2021 · 20 SEP · SHIFT 1Medium

Satellites - Orbital Velocity & Period

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is 'V'. For the satellite orbiting at an altitude of half the earth's radius, the orbital velocity is

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Answer: (c)

  1. Orbital velocity v=GMrv = \sqrt{\frac{GM}{r}}, so v∝1rv \propto \frac{1}{\sqrt{r}}.
  2. Near the surface r=Rr = R; at altitude R/2R/2, r=3R2r = \frac{3R}{2}.
  3. v′V=R3R/2=23\frac{v'}{V} = \sqrt{\frac{R}{3R/2}} = \sqrt{\frac{2}{3}}
  4. So the answer is (c) 23 V\sqrt{\frac{2}{3}}\,V.
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