Physics - Gravitation Question with Solution | TestHub

 If $v$ be the velocity in the inter planetary space and $U_{i,} U_f$ initial and final PE

Then, by the law of conservation of energy,

$U_i+K_i=U_f+K_f$

$\frac{-G{M}_{e}m}{R_e}+\frac{1}{2}m{\left(3v_e\right)}^2=0+\frac{1}{2}m{v}^2$

$\frac{-G{M}_e}{R_e}+\frac{9}{2}{v}_e^2=\frac{1}{2}{v}^2$

$\Rightarrow \frac{-2G{M}_e}{R_e}+9V_e^2=v^2$

$\Rightarrow \frac{-2g{R}_e^2}{R_e}+9v_e^2=v^2 \left[\because G{M}_e=g{R}_e^2\right]$

$-2g{R}_e+9\times 2g{R}_e=v^2 \left[\because v_e^2=2g{R}_e\right]$

$16 g{R}_{\mathit{e}}=v^2$
$\Rightarrow v=\sqrt{8}·\sqrt{2g{R}_e}=2\sqrt{2}{v}_e$