Physics - Gravitation Question with Solution | TestHub

Escape velocity,

$\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }{v}_{\mathrm{a}\mathrm{s}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{e}}=\sqrt{\frac{2 GM}{R}}\mathit{ }\mathit{ }$

$\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }\mathit{ }=R\sqrt{\frac{8}{3}\pi G\mathrm{\rho }}$

$\therefore v_e\propto R \mathrm{i}\mathrm{f}\mathrm{ }\mathrm{\rho }=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}.$

Since the planet is having double radius in comparision to earth, therefore escape velocity becomes twice$ie,$${22 \mathrm{k}\mathrm{m }\mathrm{s}}^{-1}$.