Q105 / 150 · MHT CET 2026 (17 April Shift 2) · Physics

Two planets A and B are orbiting around the sun. The distances of the two planets A and B from the sun are $r_A$ and $r_B$ respectively. Also $r_B = 225\, r_A$. If the orbital speed of the planet A is 'V' then the orbital speed of planet B will be

  • A
    $\dfrac{V}{3}$
  • B
    $\dfrac{V}{5}$
  • Correct answer
    C
    $\dfrac{V}{15}$
  • D
    $\sqrt{15}\,V$

Solution

The orbital speed of a planet revolving around the sun is given by $v = \sqrt{\dfrac{GM}{r}}$

This implies $v \propto \dfrac{1}{\sqrt{r}}$

Given $r_B = 225 r_A$ and $v_A = V$

$\dfrac{v_B}{v_A} = \sqrt{\dfrac{r_A}{r_B}}$

$\dfrac{v_B}{V} = \sqrt{\dfrac{r_A}{225 r_A}} = \dfrac{1}{15}$

$v_B = \dfrac{V}{15}$

Answer: $\dfrac{V}{15}$

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

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