Question

The velocity of escape on a planet whose radius is $ 1.7 \times 10^6\,m $ and accelaration due to gravity is $ 1.7 \,m s^{-2} $ is

• A. $ 1.7\, Km\,s^{-1} $
• B. $ 2.89\, Km\,s^{-1} $
• C. $ 1.7 \sqrt{2} km\, s^{-1} $
• D. $ 3.4\, Km\,s^{-1} $

Answer 1

Answer: (C)

Acceleration due to gravity on a planet,
$g' =1.7\,m\, s^{-2}$
Radius of planet, $r=1.7 \times 10^{6}\,m$
Escape velocity, $v_{esc}=\sqrt{2g'r}$
$=\sqrt{2\times1.7\times1.7\times10^{6}}$
$=1.7\times10^{3} \sqrt{2}\,m\,s^{-1}$
$=1.7\sqrt{2}\,km\,s^{-1}$