The escape velocity of a body from any planet whose mass is six times the mass of earth and radius is twice…

The escape velocity of a body from any planet whose mass is six times the mass of earth and radius is twice the radius of earth will be $\left(\mathrm{V}_{e}=\right.$ escape velocity of a body from the earth's surface)
  1. $\sqrt{3} \mathrm{~V}_{\mathrm{e}}$
  2. $2 \mathrm{~V}_{\mathrm{e}}$
  3. $\frac{3}{2} \mathrm{~V}_{\mathrm{e}}$
  4. $2 \sqrt{2} \mathrm{~V}_{\mathrm{e}}$

Solution

$\begin{aligned} \mathrm{V}_{\mathrm{e}} &=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \\ \mathrm{V}_{\mathrm{e}}^{\prime} &=\sqrt{\frac{2 \mathrm{G} \times 6 \mathrm{M}}{2 \mathrm{R}}} \\ &=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}} \times 3} \\ &=\sqrt{3} \mathrm{~V}_{\mathrm{e}} \end{aligned}$

Asked in: MHT CET 2020 (19 Oct Shift 2)

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