Chapter 3, Problem 55A

Gravitational force on the moon is only 1/6 that on Earth. What is the weight of a 10-kg object on the moon and on Earth? What is its mass on the moon and on Earth?

To determine

The weight and mass of the object on the moon and on Earth.

Answer to Problem 55A

The mass remains same, the weight of the object on the moon is $49\text{N}$ and on Earth is $98\text{N}$ .

Explanation of Solution

Given:

The mass of the object, $m=10\text{kg}$

The gravitational force or thereby the acceleration due to gravity on the moon,

  $\begin{array}{c}g\text{'}=\frac{1}{2}\left(g_{\text{Earth}}\right)\\ =\frac{1}{2}\left(9.8\right)\\ =4.9{\text{m/s}}^{\text{2}}\end{array}$

Formula used:

If the given mass of an object is $m$ , then the weight of the object will be,

  $W=mg$

Where, $g=$ gravity

Calculation:

The mass is the quantity of matter in an object. Hence, it will remain same on both the moon and on Earth. Now, using the above formula, the weight of the object on Earth will be,

  $\begin{array}{c}W=\left(10\right)\left(9.8\right)\\ =98\text{N}\end{array}$

And, the weight of the object on the moon will be,

  $\begin{array}{c}W\text{'}=mg\text{'}\\ =\left(10\right)\left(4.9\right)\\ =49\text{N}\end{array}$

Conclusion:

Hence, the mass of the object on both the moon and Earth remains same, while its weight on the moon is $49\text{N}$ and on Earth is $98\text{N}$ .