Question

How to calculate the mass of an object if the weight is given on the moon?

Answer 1

Step 1: Mass

1. Mass is defined as the amount or quantity of matter present inside a body.
2. Therefore, the mass of the body is independent of the place where it is measured since the amount of matter present in a body must be constant everywhere.
3. The SI unit of mass is kilograms or $kg$.

Step 2: Mass of the Object

1. The weight of an object is the force experienced by it due to the force of gravity.
2. The weight acting on an object on earth is given as $W_e=mg$, where $m$ is the mass of the object, and $g=9.8m{s}^{-2}$.
3. The gravitation force depends on the mass and radius of the planetary bodies.
4. The mass of the earth is $1000$ times the mass of the moon and the radius of the earth is $4$ times the radius of the moon.
5. Therefore, the gravitational force of attraction on earth is six times more than the gravitational force of attraction on the moon.
6. Hence, the weight of an object on Earth is six times the weight on the moon.
7. $\therefore$Weight of the object on the moon, $W_m=\frac{W_e}{6}=\frac{m\times 9.8}{6}$
8. $\therefore m=\frac{W_m\times 6}{9.8}$

Hence, if the weight of the object on the moon is given, its mass can be calculated.