Chapter 4, Problem 90A

To determine

Anexperiment to find the planet in which M has landed.

The result was shown by the scale for planet Venus and Mercury.

Answer to Problem 90A

The result was shown by the scale for the planets Venus and Mercury are $45\text{N}$ and $\text{19}\text{N}$ respectively.

Explanation of Solution

Given info:

The acceleration due tothe gravity of the planet Venus is $g_{\text{V}}=8.9\text{N/kg}$ .

The acceleration due tothe gravity of the planet Mercury is $g_{\text{M}}=3.7\text{N/kg}$ .

Formula used:

Newton’s Second Law:

The object’s acceleration is equivalent to the sum of the forces acting on the object divided by the object’s mass. That is,

  $\begin{array}{l}a=\frac{F_{\text{net}}}{m}\\ F_{\text{net}}=ma\end{array}$

Here, $m$ is the mass and $a$ is the acceleration of the object.

Calculation:

Consider that M carries a known mass of $\text{5}\text{kg}$ along with her during her interplanetary journey.

When this known mass is placed on the scale, the scale will show the different readingson different planets, as the gravitational force is dependent on the acceleration due to the gravity of the location.

The planet in which M has arrived can be determined based on the reading of the scale.

Show the analysis to find out the reading of the scale in the planets Venus and Mercury as follows:

  $\begin{array}{l}{F}_{\text{net}}=F_{\text{sm}}-F_{\text{g}}\\ ma=F_{\text{sm}}-F_{\text{g}}\\ F_{\text{sm}}=F_{\text{g}}\\ F_{\text{sm}}=mg\end{array}$

Here, $m$ is the mass of the object (in our case $5\text{kg}$ ) and $g$ is the acceleration due to the gravity of the planet concerned.

Find the scale reading corresponding to planet Mercury as follows:

  $\begin{array}{l}{\left(F_{\text{sm}}\right)}_{\text{M}}=m{g}_{\text{M}}\\ {\left(F_{\text{sm}}\right)}_{\text{M}}=5\text{kg}\times 3.7\text{N/kg}\\ {\left(F_{\text{sm}}\right)}_{\text{M}}=\text{19}\text{N}\end{array}$

Find the scale reading corresponding to planet Venus as follows:

  $\begin{array}{l}{\left(F_{\text{sm}}\right)}_{\text{V}}=m{g}_{\text{V}}\\ {\left(F_{\text{sm}}\right)}_{\text{V}}=5\text{kg}\times 8.9\text{N/kg}\\ {\left(F_{\text{sm}}\right)}_{\text{V}}=45\text{N}\end{array}$

Hence, the result shown by the scale for the planets Venus and Mercury are $45\text{N}$ and $\text{19}\text{N}$ respectively.

Conclusion:

The experiment using scales to determine the planet in which M has landed is shown.

Thus, the result shown by the scale for the planets Venus and Mercury are $45\text{N}$ and $\text{19}\text{N}$ respectively.