What is the mass of a body on the surface of the earth if its mass is 60 kg on the surface of the moon?

Figure 1. Replica of the national prototype kilogram standard no. K20 kept by the US government. It is 39 mm (1.5 inches) in diameter and 39 mm high.[1]

Mass is a measure of how much matter is contained within an object. The SI unit for mass is the kilogram.

The mass of an object can be found by pushing on it with a known force F and dividing the size of that force by the resulting acceleration (a).[2]

[math] m = \frac {F}{a} [/math]

Mass is different from weight (force) in that its value does not change if gravity changes. For example, on Earth, where the acceleration due to gravity is 9.8 m/s2, a person who has 60 kg of mass weighs 588 Newtons (132 lbs). Whereas on the moon, where the acceleration due to gravity is about 1/6 of what it is on Earth, that same 60 kg person weighs just 98 Newtons (~22 lbs).

To read more about the SI unit of mass, the kilogram, click here.

References

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Answer

Verified

Hint:-In this question, we can find the mass of the body by using the characteristic of a material. We can calculate the weight of the body with the help of relation between the gravitational forces of earth and moon.

Complete step-by-step solution:

We know that the mass of a body is a characteristic of that body. It is a universal constant and will be the same at any part of the universe. So, the mass of the body is the same on Earth and Moon and is equal to \[60kg\].But there is one more quantity which is named as weight. Weight is defined as a measure of the gravitational force on that body at that place. So, weight can be varying from place to place i.e. weight is not the characteristic of that body.A body has different values of weight at different places on Earth but this difference is very minimum so that we can ignore this difference. The gravitational force of earth i.e.${g_e}$ has a value $9.8m/{s^2}$. So, if the body has mass \[60kg\], then its weight on earth is-$ {W_e} = mg{}_e \\ \Rightarrow {W_e} = 60 \times 9.8 \\ \Rightarrow {W_e} = 588N \\ $ We know that the gravitational force on the moon is one-sixth of the gravitational force of Earth i.e.${g_m} = \dfrac{1}{6}{g_e}$ So, the weight of the body on moon will be-$ {W_m} = m{g_m} \\ \Rightarrow {W_m} = 60 \times \dfrac{1}{6}{g_e} \\ \Rightarrow {W_m} = 10 \times 9.8 \\ \Rightarrow {W_m} = 98N \\ $ So, the weight of the body on moon is $98N$

Hence, the mass of the body is \[60kg\] and the weight of the body is $98N$ on the moon.

Note:- We have to remember that the mass of a body is a universal constant and never changes at any place in the universe. For the calculation of the weight of the body, we have to keep in mind that the weight of the body on the moon is one-sixth of the weight on the earth.