Question

How is the weight of an object related to its mass?

Answer 1

- Hint: Weight is the force acting on an object on the surface of a planet due to the force of gravity acting on it. The weight of the object depends on the mass of the object and the acceleration due to gravity. It varies from one astronomical object to another.

Complete step-by-step solution -
Many of us have tried to measure our weight on a weighing machine. What this machine measures is the weight of a person or object on the surface of the earth. So, suppose if we take this machine to the moon and measure our weight again. The values shown by the weighing machines will be different for the earth and the moon. In fact, my weight on the moon will be less than my weight on earth.
This difference is because of the force of gravity acting on us on the surface of the moon and on the surface of the earth is different. So the factor that does not change in us is the mass associated with us. Mass is an inherent property of an object that doesn’t vary with the gravity acting on it.
So the weight of a body can be expressed as the product of the mass of a body and the acceleration due to gravity.
$\text{Weight}=\text{Mass}\times \left( \text{Acceleration due to gravity} \right)$
So we can express the mass of an object as,
$\text{Mass}(M)=\dfrac{W}{g}$
W is the weight of the object, g is the acceleration due to gravity.

Note: The acceleration due to the gravity of a planet of mass M and radius R is given by,
$g=\dfrac{GM}{{{R}^{2}}}$
Where, G is the gravitational constant.
M is the mass of the planet.
R is the radius of the planet.
The SI unit of g is $\text{meter}{{\left( \text{second} \right)}^{-2}}$.
The SI unit of mass is the kilogram(kg), while the SI unit of weight is the same as that of force, which is Newton (N).
A body can experience weightlessness when it is under free fall which means that the body is falling under gravity only. (Assuming there is no air resistance)