Question

The mass of Mars is $\mathbf{6}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{23}}\mathbf{}$and its radius is $\mathbf{}\mathbf{3}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}\mathbf{\hspace{0.33em}}\mathbf{m}$. What is the value of constant g on Mars?

Short answer

The value of constant g on mars is $3.709\hspace{0.33em}\mathrm{m}/{\sec }^2.$

Step-by-step solution

Identification of the given data

The given data can be listed below as,

• The mass of Mars is,$\mathrm{m}=6.4\times {10}^{23}\mathrm{kg}$.
• The radius of Mars is, $\mathrm{r}=3.4\times {10}^6\mathrm{m}$.
• Assume universal gas constant (G) =$6.7\times {10}^{-11}$

Significance of Newton’s second law on a sled

This law states that the force acting on Mars depends on Mars’s mass and mars acceleration.

The mass of Mars and acceleration of the Mars product give the force required to accelerate Mars.

Determination of acceleration due to gravity on Mars.

Let g be acceleration due to gravity on Mars.

As we know that according to the second law of motion,

F = mg …………………….(1)

Also, according to universal gravitational law,

$F=G\frac{Mm}{r^2}$ …………………….(2)

Now, 1 = 2,

Therefore,

$$\begin{gathered} mg=G\frac{Mm}{r^2} \\ g=\frac{GM}{r^2} \end{gathered}$$

$$\begin{gathered} g=\frac{6.7\times {10}^{-11}\times 6.4\times {10}^{23}}{{\left(3.4\times {10}^6\right)}^2} \\ =\frac{6.7\times 6.4\times {10}^{-11+23-6-6}}{3.4\times 3.4} \\ =42.88\times {10}^0 \\ =3.709 \end{gathered}$$

Thus, the value of constant g on Mars is $3.709\hspace{0.33em}\mathrm{m}/{\sec }^2$