If the radius of a planet is 'R' and density ' $\varrho$ ', then the escape velocity '$V_e$' of anybody from…

If the radius of a planet is 'R' and density ' $\varrho$ ', then the escape velocity '$V_e$' of anybody from its surface will be proportional to
  1. $\mathrm{R}$
  2. $\frac{\sqrt{\varrho}}{\mathrm{R}}$
  3. $\mathrm{R} \sqrt{\rho}$
  4. $\frac{\mathrm{R}}{\sqrt{\rho}}$

Solution

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

Asked in: MHT CET 2020 (20 Oct Shift 1)

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