The escape velocity for a planet whose mass is six times the mass of earth and the radius is twice the…
The escape velocity for a planet whose mass is six times the mass of earth and the radius is twice the radius of earth will be $\left[\mathrm{V}_{\mathrm{e}}=\right.$ escape velocity from the earth $]$
$\sqrt{2} \mathrm{~V}_{\mathrm{e}}$
$\frac{1}{2} \mathrm{~V}_{\mathrm{e}}$
$\sqrt{3} \mathrm{~V}_{\mathrm{e}}$
$2 \sqrt{2} \mathrm{~V}_{\mathrm{e}}$
Solution
Escape velocity is defined using relation:
$\begin{aligned} & \frac{1}{2} \mathrm{mv}_{\mathrm{e}}^2=\frac{\mathrm{GMm}}{\mathrm{R}} \\ & \Rightarrow \mathrm{V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}\end{aligned}$
If $M$ is replaced $6 M \& R$ is replaced by $2 R$ then
$\mathrm{V}_{\mathrm{e}}^{\prime}=\sqrt{3} \mathrm{~V}_{\mathrm{e}}$