Mass and Weight

In this article, we are going to learn about the concepts of mass and weight, as well as that of centre of gravity.

Table of Contents

• What are Mass and Weight?
• Centre of Gravity

What are Mass and Weight?

• The mass of a body is the quantity of matter contained in it.
• The weight of body is the force with which it is attracted towards the centre of a celestial body (e.g. earth), i.e. it refers to the force of the gravitational pull.

What is the difference between Mass and Weight?

• While mass is a scalar quantity, weight is a force and so it’s a vector quantity.

• Mass of a body is its own characteristic – it is not dependent on outer factors. That’s why mass of a body is considered constant. It won’t change from place to place. However, as weight depends on the strength of the external gravitational force as well as the mass, it varies from one place to another; it’s not constant. This will become clearer if we see the formula of weight.
  
  Weight of a body, w = mg, where g is the acceleration due to gravity due to an external celestial body and m is the mass of the body.
  
  As g varies from one place to another (even on the surface of the earth), it’s obvious that the value of weight will vary.

• SI unit of mass is kg, while the SI unit of weight is newton (N).

• To measure mass, we use an ordinary equal arm balance. While to measure weight, we use a spring balance.
  

If a body has a mass of 1 kg, then its weight on earth will be around 9.8 N. This is the force of gravity by which the earth will be pulling this body towards its centre.

Weight of a Body in a Lift

The weight of a body varies as acceleration due to gravity changes. This is what happens in a lift. Let us consider the weight of the body at the surface of the earth as its true weight. Let’s see how its apparent weight varies in a lift.

• If a lift is stationary or moving with uniform speed (either upward or downward), then obviously its acceleration would be zero. The body will feel the normal g force of the earth. So, Apparent weight = True weight.
• If lift if going up with acceleration, then the body will feel more g force. So, Apparent weight > True weight.
• If lift if going down with acceleration, then the body will feel less g force. So, Apparent weight < True weight.
• If the lift starts falling freely, i.e. with an acceleration equal to the acceleration due to gravity (g), then the body inside it will feel no g force. So, Apparent weight = 0. That is, the body will feel weightlessness.

Centre of Gravity

Centre of Gravity (C.G.) of a body is the point at which the whole weight of the body appears to act.

Here are some more points you should know about centre of gravity:

• Centre of Gravity of a body need not always be inside the material of the body. It can also lie outside it.
• In case of a regularly shaped body, the centre of gravity lies at its geometrical centre.

Universal conditions for stability of equilibrium

For a body to be at stable equilibrium, it should fulfil certain conditions:

• The body must have minimum possible potential energy. For this to happen, its centre of gravity must lie as low as possible.
• The vertical line through the centre of gravity of the body must pass through the base of the body.

Applications of Centre of Gravity

• Sometimes building lean a bit but do not fall down, e.g. Tower of Pisa. They remain stable because the vertical line passing through their centre of gravity lies within the base of their body. This is also the reason behind people leaning on the other side of the weight they carry. For example, when we carry a huge weight (say a water bucket) with our right hand, our body leans towards the left, so as to ensure that the vertical line passing through centre of gravity of the entire system (man + bucket) passes through the base of the system (space between our feet).

• If centre of gravity of a system is too much above the ground, it may become unstable and topple over. For example, a double-decker bus may overturn if more passengers are seated on the upper deck. That’s because in such a scenario the centre of gravity of the entire system (bus + passenger) will be shifted upward and the stability of equilibrium will be reduced.