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The mass of a planet is $\frac{1}{10}$th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:
A
$4.9\ \text{m s}^{-2}$
B
$3.92\ \text{m s}^{-2}$
C
$19.6\ \text{m s}^{-2}$
D
$9.8\ \text{m s}^{-2}$
Detailed Solution
Acceleration due to gravity $g = \frac{GM}{R^2}$
For the planet: $M' = \frac{M}{10}$, $R' = \frac{R}{2}$
$g' = \frac{G(M/10)}{(R/2)^2} = \frac{4GM}{10R^2} = \frac{4}{10}g$
$g' = \frac{4}{10} \times 9.8 = 3.92\ ms^{-2}$