Question

How the weight of an object on Earth is six times the weight on the moon?

Answer 1

Explanation of Weight:

1. As we know that the mass of a body is constant everywhere, the mass of an object on earth is not six times the mass on the moon.
2. Rather is the weight that differs depending on its position.
3. The weight of an object is the force experienced by it due to the force of gravity.
4. The gravitational force on earth is six times greater than the gravitational force on the moon.
5. This is because gravitation force depends on the mass and radius of the planetary bodies.
6. If $G$ is the universal gravitational constant, $M$ is the mass of the moon, $m$ is the mass of the object, $R$ is the radius of the planetary object, then the formula for the gravitational force exerted by the moon is given as: $F=\frac{GMm}{R^2}$
7. The mass of the earth $\left(M_e\right)$ is $100$ times the mass of the moon and the radius of the earth is $4$ times the radius of the moon.
8. The gravitational force exerted by the Earth will be: $F=\frac{100G{M}_{e}m}{{\left(4R\right)}^2}=6.25\frac{G{M}_{e}m}{R^2}$
9. Therefore, the gravitational force of attraction on earth is six times more than the gravitational force of attraction on the moon.

Hence, the weight of an object on Earth is six times the weight on the moon.