Q106 / 150 · MHT CET 2025 (21 Apr Shift 2) · Physics

The radii of circular orbits of two satellites $A$ and $B$ of the earth are ' $4 R$ ' and ' $R$ ' respectively, where $R$ is the radius of earth. If the speed of satellite $B$ is 6 V , then the speed of satellite $A$ will be

  • Correct answer
    A
    3 V
  • B
    4 V
  • C
    12 V
  • D
    $\frac{3}{4} \mathrm{~V}$

Solution

The orbital speed for a satellite is given by $v = \sqrt{\frac{GM}{r}}$, where $r$ is the orbital radius.
For satellite B with $r_B = R$ and $v_B = 6V$, we have $6V = \sqrt{\frac{GM}{R}}$.

Satellite A orbits at $r_A = 4R$, so its speed is $v_A = \sqrt{\frac{GM}{4R}} = \frac{1}{2}\sqrt{\frac{GM}{R}}$.

Substituting from the satellite B expression gives $v_A = \frac{1}{2}(6V) = 3V$.

Final answer: $\boxed{3V}$

Hence, the correct answer is option: 'A'.

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