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Physics
What is the escape velocity for a body on the surface of a planet on which the acceleration due to gravity is (3.1)2 ms-2 and whose radius is 8100 km?
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Q. What is the escape velocity for a body on the surface of a planet on which the acceleration due to gravity is $(3.1)^2 ms^{-2}$ and whose radius is 8100 km?
KEAM
KEAM 2006
Gravitation
A
$2790\, km-s^{-1}$
12%
B
$27.9\,km-s^{-1}$
31%
C
$\frac{27.9}{\sqrt5}\,km^{-1}$
45%
D
$27.9\sqrt5 \,km-s^{-1}$
11%
Solution:
Escape velocity $v_e=\sqrt{2gR}$
Given, $g=(3.1)^2ms^{-2},$
$R = 8100km = 8 1 00 x 10^3 m.$ = $v_e=\sqrt{2\times(3.1)^2\times8100\times10^3}$
$v_e=12.5\times10^3ms^{-1}$
$\Rightarrow v_e=12.5 kms^{-1}$
$\approx\frac{27.9}{\sqrt5}kms^{-1}$