Q103 / 150 · MHT CET 2020 (20 Oct Shift 1) · Physics

If the radius of a planet is 'R' and density ' $\varrho$ ', then the escape velocity 'Ve' of any body from its surface will be proportional to

  • A
    $\mathrm{R}$
  • B
    $\frac{\sqrt{\varrho}}{\mathrm{R}}$
  • Correct answer
    C
    $\mathrm{R} \sqrt{\rho}$
  • D
    $\frac{\mathrm{R}}{\sqrt{\rho}$

Solution

$v_{e}=\sqrt{\frac{G M}{R}}=\sqrt{\frac{G \frac{4}{3} \pi R^{3} \rho}{R}}=k R \sqrt{\rho}$ $v_{e} \propto R \sqrt{\rho}$

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

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