Question

The radius of the earth is 6370 km and radius of mars is 3440 km. What is the acceleration
due to gravity on mars if mass of the mars is 0.11 times the mass of earth?
​

Answer 1

Answer:

The acceleration due to gravity on mars is 3.7m/s²

Step by step explanation:

Radius of the earth ($\textbf{r}_\textbf{e}$) = 6370 km

Radius of mars ($\textbf{r}_\textbf{m}$) = 3440 km

Mass of mars = 0.11 × Mass of the earth

$\Rightarrow \text{M}_\text{m}=0.11\times \text{M}_\text{e}$

Acceleration due to gravity is given by the formula

$\Rightarrow \textbf{Acceleration due to gravity(g) = }\frac{\textbf{GM}}{\textbf{R}^2}$

For Earth:

$\Rightarrow \text{g}_\text{e}=\frac{\text{GM}_e}{\text{R}^2}$

$\Rightarrow \text{g}=\frac{\text{GM}_e}{\text{(6370)}^2}\ \ \ \ \ .....(1)$

For Mars:

$\Rightarrow \text{g}_\text{m}=\frac{\text{GM}_\text{m}}{\text{(3440)}^2}$

$\Rightarrow \text{g}_\text{m}=\frac{\text{G(M}_e\times0.11)}{\text{(3440)}^2}\ \ \ \ \ .....(2)$

From equations (1) & (2), we get

$\Rightarrow\frac{\text{g}}{\text{g}_\text{m}} =\frac{\frac{\text{GM}_e}{\text{(6370)}^2}}{\frac{\text{G(M}_e\times0.11)}{\text{(3440)}^2}}$

$\Rightarrow\frac{\text{g}}{\text{g}_\text{m}} =\frac{(3440)^2}{(6370)^2\times 0.11}$

$\Rightarrow\frac{\text{g}}{\text{g}_\text{m}} =2.65$

$\Rightarrow \text{g}_\text{m}=\frac{9.81}{2.65}$

$\Rightarrow \text{g}_\text{m}=3.7 \text{ m/s}^2$

$\boxed{\text{The acceleration due to gravity on mars is 3.7m/s}^2}$