GravitationMedium
Question
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:
Options
A.$4.9\text{ }m{\text{ }s}^{- 2}$
B.$3.92\text{ }m{\text{ }s}^{- 2}$
C.$19.6\text{ }m{\text{ }s}^{- 2}$
D.$9.8\text{ }m{\text{ }s}^{- 2}$
Solution
Sol. [Key Concept: Acceleration due to gravity on a planet (g ∝ M/R²)]
$$g^{'} = \frac{GM^{'}}{R^{'2}} = \frac{GM}{10\left( \frac{R}{2} \right)^{2}}$$
$$\begin{matrix} & \ = \frac{4}{10}\frac{GM}{R^{2}} = 0.4 \times 9.8 \\ & \ = 3.92\text{ }m{\text{ }s}^{- 2} \end{matrix}$$
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