The mass of a planet is six time that of the earth. The radius of the planet is twice that of the earth. If…

The mass of a planet is six time that of the earth. The radius of the planet is twice that of the earth. If the escape velocity from the earth is ' $\mathrm{V}_{\mathrm{e}}$ ', then the escape velocity from the planet is
  1. $\sqrt{3} \mathrm{~V}_{\mathrm{e}}$
  2. $\sqrt{2} \mathrm{~V}_{\mathrm{e}}$
  3. $\mathrm{V}_{\mathrm{e}}$
  4. $\sqrt{5} \mathrm{~V}_{\mathrm{e}}$

Solution

$\begin{aligned} & V_e=\sqrt{\frac{2 G M}{R}} ; V_p=\sqrt{\frac{2 \mathrm{GM}_p}{R_p}} \\ & \therefore \frac{V_p}{V_e}=\sqrt{\frac{M_p}{M}} \cdot \frac{R}{R_p}=\sqrt{6 \times \frac{1}{2}}=\sqrt{3} \\ & \therefore V_p=\sqrt{3} V_e\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 1)

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