Question

The escape velocity from the surface of the earth is $ 11.2\,km\,s^{-1} $ . What is the escape velocity in a planet whose radius is three times that of the earth and on which the acceleration due to gravity is three times of that on the earth?

• A. $ 11.2\,km\,s^{-1} $
• B. $ 22.4\,km\,s^{-1} $
• C. $ 33.6\,km\,s^{-1} $
• D. $ 5.6\,km\,s^{-1} $

Answer 1

Answer: (C)

Escape speed on the earth surface $v_{e}=\sqrt{2 g_{e} R_{e}}$
$ 11.2=\sqrt{2 g_{e} R_{e}} . .$ (i)
Escape speed on the planet surface
$v_{p}=\sqrt{2 g_{p} R_{p}} $
$=\sqrt{2\left(3 g_{e}\right)\left(3 R_{e}\right)} $
$[\because g_{p}=3 g_{e} \,\, R_{p}=3 R_{e}]$
$=3 \sqrt{2 g_{e} R_{e}} $
$V_{p}=3 V_{e}=33.6 \,m / s$