# Mass and Weight

MASS AND WEIGHT

Mass

It is one of the fundamental quantities in Physics and the most basic property of matter. We can define mass as the measure of the amount of matter in a body. The SI unit of mass is Kilogram (kg).

Note: The mass of a body does not change at any time. Only for certain extreme cases when a huge amount of energy is given or taken from a body. For example: in a nuclear reaction, tiny amount of matter is converted into a huge amount of energy, this reduces the mass of the substance.

Weight

It is the measure of the force of gravity acting on a body.

The formula for weight is given by:

w = mg

As weight is a force its SI unit is also the same as that of force, SI unit of weight is Newton (N). Looking at the expression of weight we see that it depends on mass and the acceleration due to gravity, the mass may not change but the acceleration due to gravity does change from place to place. To understand this concept let’s take this example,

Shape of the earth is not completely spherical, but an oblate spheroid, therefore a person standing at the equator is far away from the center of the earth than a person standing at the north pole, as acceleration due to gravity is proportional to the inverse of the square of the distance between two objects, a person standing at the north pole would experience more weight as he is closer to the center of the earth than a person standing at the equator.

Relation between Weight and Mass

Consider a body having large mass and large weight. Example of this situation is a large object which is hard to throw because the weight of this object is large.

Therefore, the relation between weight and mass can be derived with the help of  Newton’s second law  which explains that the free falling object has an acceleration “g” as the magnitude.

If an object with a mass of 1kg falls with an acceleration of 9.8 ms-2, then the magnitude of the force is given as :

F = ma
= (1kg)(9.8ms-2)
= (9.8 kg.ms-2)
= 9.8 N

## What is the Difference between Mass and Weight?

Weight of the moon:
Suppose a body of mass "m" and its weight on the moon is  $W_m$Wm .
Mass of the moon is "M" and its radius is "R"

Weight of an object on the moon = Force with which the moon pulls.
$W_m=G$Wm=G $\frac{Mm}{R^2}$MmR2
The weight of the same object on the earth is  $W_e$We
Mass of the earth is 100 times of that of the moon.

Radius of the moon = R

Radius of the Earth = 4R

Weight of the object on the earth =    $W_e=G$We=G $\frac{100Mm}{\left(4R\right)^2}$100Mm(4R)2

$W_e=G$We=G $\frac{100Mm}{16R^2}$100Mm16R2

$\frac{W_m}{W_e}=\frac{\frac{GMm}{R^2}}{\frac{G100Mm}{16R^2}}=\frac{16}{100}\approx\frac{1}{6}$WmWe =GMmR2 G100Mm16R2  =16100 16

Thus the weight on the moon is 1/6 the weight on the earth.