Chapter 7, Problem 73A

To determine

The weight of a person on the planet Mars if it weighs $637\text{N}$ on Earth’s surface.

Answer to Problem 73A

  $240.5\text{N}$

Explanation of Solution

Given:

Mass of the Mars is $6.42\times {10}^{23}\text{}\text{kg}$

Radius of the Mars is $3.40\times {10}^6\text{}\text{m}$ .

The weight of the person on Earth’s surface is $637\text{N}$ .

Formula used:

The value of g on any planet can be obtained by:

  $g=\frac{GM}{R^2}$

Where, $G$ is the gravitational constant, $R$ is the radius of the planet, and $M$ is the mass of the planet.

Calculation:

The value of gravitational constant is,

  $G=6.67\times {10}^{-11}\text{N}{\text{.m}}^{\text{2}}{\text{/kg}}^{\text{2}}$

Then using the given values of mass and radius of the Mars, the value of $g\text{'}$ will be,

  $\begin{array}{c}g\text{'}=\frac{GM}{R^2}\\ =\frac{6.67\times {10}^{-11}\times 6.42\times {10}^{23}}{{\left(3.40\times {10}^6\text{}\text{m}\right)}^2}\\ =3.70{\text{m/s}}^2\end{array}$

Now, it is given that weight of the person on Earth is $637\text{N}$ , and the value of $g$ on Earth is $9.8\text{}{\text{m/s}}^{\text{2}}$ , then the mass of the person will be,

  $\begin{array}{c}W=mg\\ 637=m\times 9.8\\ m=65\text{kg}\end{array}$

Then, the weight of the person on the Mars is,

  $\begin{array}{c}W\text{'}=mg\text{'}\\ =65\times 3.70\\ =240.5\text{N}\end{array}$

Conclusion:

Thus, the weight of the person on the Mars is $240.5\text{N}$ .