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If the escape velocity on earth is $11.2 \mathrm{~km} / \mathrm{s}$, its value for a planet having double the radius and 8 time the mass of earth is
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22.4 km/s
Escape velocity of an object on a planetary body,
$v_e=\sqrt{\frac{2 G M}{R}} \Rightarrow v_e \propto \sqrt{\frac{M}{R}}$
So, $\begin{aligned} \frac{\left(v_e\right)_1}{\left(v_e\right)_2} & =\frac{\sqrt{\frac{M_1}{R_1}}}{\sqrt{\frac{M_2}{R_2}}} \Rightarrow \frac{\left(v_e\right)_1}{\left(v_e\right)_2}=\sqrt{\frac{M_1}{M_2} \times \frac{R_2}{R_1}} \\ \frac{11.2}{\left(v_e\right)_2} & =\sqrt{\frac{M}{8 M} \times \frac{2 R}{R}} \Rightarrow \frac{11.2}{\left(v_e\right)_2}=\sqrt{\frac{1}{4}} \Rightarrow \frac{11.2}{\left(v_e\right)_2}=\frac{1}{2} \\ \left(v_e\right)_2 & =2 \times 11.2 \Rightarrow\left(v_e\right)_2=22.4 \mathrm{~km} / \mathrm{s}\end{aligned}$
$v_e=\sqrt{\frac{2 G M}{R}} \Rightarrow v_e \propto \sqrt{\frac{M}{R}}$
So, $\begin{aligned} \frac{\left(v_e\right)_1}{\left(v_e\right)_2} & =\frac{\sqrt{\frac{M_1}{R_1}}}{\sqrt{\frac{M_2}{R_2}}} \Rightarrow \frac{\left(v_e\right)_1}{\left(v_e\right)_2}=\sqrt{\frac{M_1}{M_2} \times \frac{R_2}{R_1}} \\ \frac{11.2}{\left(v_e\right)_2} & =\sqrt{\frac{M}{8 M} \times \frac{2 R}{R}} \Rightarrow \frac{11.2}{\left(v_e\right)_2}=\sqrt{\frac{1}{4}} \Rightarrow \frac{11.2}{\left(v_e\right)_2}=\frac{1}{2} \\ \left(v_e\right)_2 & =2 \times 11.2 \Rightarrow\left(v_e\right)_2=22.4 \mathrm{~km} / \mathrm{s}\end{aligned}$
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