Q97 / 125 · BITSAT 2010 · Physics

Two planets $\mathrm{A}$ and $\mathrm{B}$ have the same material density. If the radius of $\mathrm{A}$ is twice that of $\mathrm{B}$, then the ratio of the escape velocity $\mathrm{v}_{\mathrm{A}} / \mathrm{v}_{\mathrm{B}}$ is

  • Correct answer
    A
    2
  • B
    $\sqrt{2}$
  • C
    $1 / \sqrt{2}$
  • D
    $1 / 2$

Solution

$v_{e}=\sqrt{2 g R}=\sqrt{\frac{2 G M}{R^{2}}} R=\sqrt{\frac{2 G d \frac{4}{3} \pi R^{3}}{R^{2}}} R$ $=\mathrm{R} \sqrt{2 \mathrm{Gd} \frac{4}{3} \pi}$ as $v_{e} \propto R$ for same density, $\frac{v_{A}}{v_{B}}=2$

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

Relevant Questions