MASS AND WEIGHT

What is Mass?
The quantity of matter present in a body is called Mass. It remains unchanged irrespective of the shape, volume or position of the body. Its numerical value remains constant. It is a fundamental property of a body and numerical measure of inertia. In physics, we can classify mass into two types namely gravitational mass and inertial mass.
If we compare the masses of the body by using a beam balance against standard masses then the gravitational mass of a body could be determined. This is done to eliminate the gravitational factor. The measure of a body’s resistance to its acceleration while responding to some external force is called inertial mass.
The symbol to represent mass is m and the SI unit of mass is kilogram
                                          

What is Weight?

The force exerted by the gravity on a body due to which it is pulled towards the Earth is called the weight of a body. It is measured by mass of a body times the acceleration due to gravity.

W = mg

where, W = Weight of a body

M = Mass of the body

g = Acceleration due to gravity. The value of it on Earth has a constant value of 9.8 m/s2 

The weight of a body varies at different places as it depends on acceleration due to gravity. The weight of a body on Earth would remain constant whereas the weight on moon would change as the acceleration due to gravity on moon is one-sixth to that of Earth.

                       

WEIGHT (W) = MASS(M) X ACCELERATION DUE TO GRAVITY(g)

Relation Between Mass & Weight

The relation between mass and weight of a body is defined by Newton’s Second Law of Motion. The law as stated by Newton goes by “Force is equal to the change in momentum (mv)per change in time. For a constant mass, force equals mass times acceleration”

F = m×a

F = Force
m = mass
a = acceleration

When this acceleration ‘a’ is due to gravity ‘g’ then the force applied on or exerted by the body becomes the weight of the body

Weight of the body = Mass of the body ×× Acceleration due to gravity

Example: Calculate the weight of a body given the mass of the body = 4kgs

Solution: Weight of the body = Mass ×$\times$ Acceleration = 4kgs×9.8m/s2= 39.2N

Unit of Mass & Weight:

The international system ff units (SI)of mass is kilogram and that of weight is Newton. The Centimeter-Gram-Second (CGS)unit of mass is gram and that of weight is Dyne

Kilogram and gram are the basic unit of mass. While kilogram is the unit of mass of larger body having a greater quantity of matter, a gram is the unit of mass of smaller body having less amount of matter. 

Relation between mass and weight:

1 kilogram = 1000 grams

Newton is the SI unit of force. It is the amount of force required by a body of mass one kilogram to produce an acceleration of one meter per Second Square
Dyne is the CGS unit of force. It is the amount of force required by a body of mass one gram to product an acceleration of one centimeter per square second

Relation between Newton and Dyne:

1 Newton = 1,00,000 Dyne= 105 Dyne

Effect of Gravity

Effect of gravity on mass – Mass of a body is constant irrespective of its place and position. There is no effect of gravity on mass. It remains the same be it on Earth or any other planet like Moon even though the acceleration due to gravity value keeps on changing at different planets

Effect of gravity on weight – Weight is how heavy an object is in a gravitational field. The weight of a body keeps on decreasing at higher altitude where it is furthest away from the center of gravity of Earth. They are directly proportional to each other. The acceleration due to gravity on Moon is one-sixth to that of Earth so the weight also becomes 16 ,16th to that on Earth.

Difference Between Mass & Weight

Definition: Mass is defined as the amount of matter with which it is made up of, regardless of its configuration or any force acting on the body. Weight is the computation of the force of gravity acting on a body and it depends on the value of acceleration due to the gravity of the place in which the body resides.

Gravitational effect: Mass of a body being constant at any place is unaffected by the gravity whereas weight of an object is directly proportional to the value of gravity of that place.

Unit of Measurement: The S.I and C.G.S unit of mass is kilogram and gram respectively whereas that of weight is Newton and dyne respectively.

Device used for measurement: For mass the device used for measurement could be lever balance, beam balance, pan balance or any electronic device whereas the device used for measuring weight is spring balance.

Type of quantity: Mass is a scalar quantity having the only magnitude of the body whereas weight is a vector quantity having both magnitude of the body and direction of the force.

Examples

i) Calculate the weight of a car with a mass of 1000 kg. Given, gravity on the Earth's surface is 10 newtons per kilogram

Solution: 
Weight = Mass ×$\times$ Gravity

           = 1000 ×$\times$ 10

   = 10,000 Newtons

ii) An astronaut has a mass of 50 kg on Earth, what is the astronaut's mass on the Moon? Given, gravity on the Moon is 1.6 newtons per kilogram.

Solution:

Mass is independent of place or position, so the astronaut's mass on the Moon and that on Earth is the same

Therefore, Astronaut's mass on the Moon = Astronaut's mass on the Earth

 
                                                             = 50 kgs