The escape velocity for earth is $v$. A planet having 9 times mass that of earth and radius, 16 time

Question

The escape velocity for earth is $v$. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of

Professor PC Thomas Classes · Answer

(c) : The escape velocity of Earth, $ \begin{aligned} v & =\sqrt{\frac{2 G M_e}{R_e}}=\sqrt{\frac{2 G 	imes 9 M_e}{16 R_e}} & & \ \left(\begin{array}{rr} \because  M_p=9 M_e \ R_p=16 R_e \end{array}ight) \ & =\frac{3}{4} \sqrt{\frac{2 G M_e}{R_e}} \Rightarrow v_p=\frac{3}{4} v & & 	ext { (using above eqn.) } \end{aligned} $