Escape velocity of a body from earth is 11 . 2km s ^ - 1 . If the...

Given: ${R}_{P} = \dfrac{{R}_{E}}{3}, {M}_{P} = \dfrac{{M}_{E}}{6}$

Escape velocity is given by, $v = \sqrt{\dfrac{2GM}{R}}$

Therefore,

${v}_{E} = \sqrt{\dfrac{2G{M}_{E}}{{R}_{E}}} . . . ( i )$

${v}_{P} = \sqrt{\dfrac{2G{M}_{P}}{{R}_{P}}} . . . ( ii )$

$⇒ \dfrac{{v}_{E}}{{v}_{P}} = \sqrt{2}$

$⇒ {v}_{P} = \dfrac{{v}_{E}}{\sqrt{2}} = \dfrac{11 . 2}{\sqrt{2}} = 7 . 9km{s}^{- 1}$