Difference Between Mass and Weight

Mass and weight are often used interchangeably for common purposes but in physics, these two concepts refer to different quantities. However, mass and weight are very closely related. Mass is the manifestation of the amount of matter present in an object. A physical body cannot have zero mass. Any massive body feels a force due to the gravitational field of another massive object. This force is called weight. Weight is proportional to the mass of an object. The amount of substance in an object is measured in mass, whereas the force applied to it is measured in weight. 

The weight of a body changes if the gravitational field strength changes, however, its mass remains invariant. For instance, an object weighs differently on the Earth and Mars but its mass remains the same. For example, because the ball is afloat in water, we can deduce that its weight is zero. However, the weight is not zero in this scenario. The buoyancy attribute is used instead. This necessitates a greater grasp of mass and weight.

Definition of Mass and Weight

The mass of a body is an intrinsic property that is a measure of its inertia. It quantifies the amount of resistance a body offers in an attempt to change its state of motion. According to the theory of relativity, mass and energy are equivalent. Mathematically, mass can be defined from Newton’s second law. If the acceleration of a body is a due to a force F, then its mass m is given by

\[m=\frac{F}{a}\]

Mass is the manifestation of the amount of matter present in an object. A physical body cannot have zero mass. A massive body feels attraction due to gravity. The amount of force exerted by a gravitational field (e.g. the Earth’s gravity) on an object is called its weight. Gravitational acceleration is independent of the object on which a gravitational force is acting. If the gravitational acceleration due to the Earth’s gravitational field is g, the weight W of an object of mass m is given by the gravitational force acting on it,

W = Fg= mg

Since the weight of a body depends on the gravitational field, a body with the same mass can have different weights at different places. The weight of a massive object can even be zero.

Mass and Weight Difference

Solved Example

1. An object of mass 1 kg is suspended from a spring balancing apparatus with a gravitational acceleration being 10 m/s2. What would be the reading of the instrument if the spring moves with acceleration 5 m/s2 in the (a) upward, (b) downward direction?

Solution: Gravitational acceleration acts downwards having magnitude g = 10 m/s2.

When a force apart from gravity acts on a body, its weight changes apparently. The apparent weight is the product of mass and net acceleration of the body. The object in the given problem has mass m = 1kg. 

a. When the apparatus moves upwards with acceleration a = 5 m/s2, resultant downward acceleration is g-(-a) = g + a. Hence the apparent weight is,

 Wa= m(g + a)

 Wa = 1(10 + 5) N

 Wa=  15 N

 The reading of the instrument gives, 

\[\frac{W_{a}}{g}\]= 1.5 kg  

b. When the apparatus moves downwards with acceleration a = 5 m/s2, resultant downward acceleration is g - a. Therefore, the apparent weight is,

Wb= m(g - a)

Wb= 1(10 - 5) N

Wb=5N

The instrument reads,

\[\frac{W_{b}}{g}\]= 0.5 kg

In this problem, the weight of the body differs in two different situations although the mass remains the same.

2. The gravitational force on the moon's surface is just 1/6th as powerful as it is on Earth. What is the weight of a 10-kilogram object on the moon compared to the earth in Newtons?

 Solution:  The Mass of the object = 10 kg

   Object’s weight on the earth = W = m × g

        ∴ W = 10 × 9.8

                W = 98 N

 The weight of the object on the moon is equal to 1/6th the weight on the earth.

Because the gravitational force on the surface of the moon is only 1/6th as powerful as that on the earth's surface.

Weight of the object on the moon =

Weight on earth = 98 N

Weight on moon = 16.3 N

Did You know?

• The weight of an object can apparently increase or decrease inside a fluid but the mass would remain the same. In the absence of the Earth’s atmosphere, everything would be a little heavier (although we would not be alive to verify that!). 

• Objects weigh differently on different planets (e.g. an astronomer’s weight is less on the Moon than that of the Earth) because the gravitational accelerations are not equal.

• An object floating on a liquid or an astronomer in space has zero weight.

This is because the mass of a body is determined by the volume occupied by the body, and the weight represents the energy of that object in relation to the attraction of gravity on another object (According to the law of gravitation). Our weight on land is determined by the force with which the earth attracts us to the ground. Because we do not weigh the same at the top of a mountain as we do at sea level, we use global standards to avoid errors due to the small difference. It is worth noting, however, that our body weighs less in water due to buoyancy, which is a force that opposes gravity.