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For a planet having mass equal to mass of the earth but radius one fourth of radius of the earth, then escape velocity for this planet will be
A
11.2 km/s
B
22.4 km/s
C
5.6 km/s
D
44.8 km/s
Detailed Solution
Escape velocity: $v_{es} = \sqrt{\dfrac{2GM}{R}}$; for the earth, $v_{es} = 11.2$ km/s.
For the planet, $M' = M_e$ and $R' = \dfrac{R_e}{4}$:
$v'_{es} = \sqrt{\dfrac{2GM_e \times 4}{R_e}} = 2\sqrt{\dfrac{2GM_e}{R_e}}$
$v'_{es} = 2 \times 11.2 = 22.4$ km/s
For the planet, $M' = M_e$ and $R' = \dfrac{R_e}{4}$:
$v'_{es} = \sqrt{\dfrac{2GM_e \times 4}{R_e}} = 2\sqrt{\dfrac{2GM_e}{R_e}}$
$v'_{es} = 2 \times 11.2 = 22.4$ km/s