 # Difference Between Mass and Weight

Mass and Weight

Mass and weight are often used interchangeably in 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 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.

Definition of Mass and Weight

Mass of a body is an intrinsic property which is a measure of its inertia. It quantifies the amount of resistance a body offers to 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 = F$_{g}$ = 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.

The comparison between mass and weight in the following table shows the basic differences between the quantities.

## Mass and Weight Difference

 Context Mass Weight Defining property Mass is defined by the amount of acceleration an object feels when a force is acted upon. Any object having mass feels a force of attraction in a gravitational field. The gravitational force is called the object’s weight. Type of quantity Mass is a fundamental or base quantity. Weight is a derived quantity. Dimension [M] Weight has the dimension of force which is (mass acceleration). The dimension is [MLT-2] Physical quantity type (scalar or vector) Mass is a scalar quantity since it only has magnitude. Weight is a vector quantity since it is represented by a force. Units SI unit: kilogram (kg)CGS unit: gram (g)FPS unit: pound (lb) SI unit: Newton (N) orkgms-2CGS unit: dyne (dyn) or gcms-2FPS unit: poundal (pdl) or  lbfts-2 Effect of gravity Since mass is an intrinsic property, it does not depend on gravity. Mass of a physical body always remains constant if the body does not emit or absorb energy by any means. Weight changes with the gravitational field as it is proportional to the gravitational acceleration. Zero gravity condition The mass of an object is not zero when it is not in a gravitational field. Weight is zero in a zero gravitational field. For instance, during an ideal free fall or in space, the weight of a massive body is effectively zero. Presence of forces other than gravity Following the definition of mass, it can never change under such conditions. Forces other than gravity can cause an apparent change in the weight of an object. Some examples are,Buoyant force due to a fluid can change the weight of an immersed body apparently.The weight of a body inside an accelerating lift can change. It becomes heavier if the acceleration is upwards and it becomes lighter if the acceleration is downwards.During a free fall (downward acceleration equal to gravitational acceleration), a body effectively becomes weightless. Instruments of measurement Mass can be measured using various balancing methods. It can also be determined by measuring weight.Mass of subatomic charged particles having very small mass can be measured using electric and magnetic fields. Weight is generally measured using a spring balance.

Solved Example

1. An object of mass 1 kg is suspended from a spring balancing apparatus with 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.

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

W$_{a}$ = m(g + a)

W$_{a}$ = 1(10 + 5) N

W$_{a}$ =  15 N

The reading of the instrument gives,

$\frac{W_{a}}{g}$ = 1.5 kg

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

W$_{b}$ = m(g - a)

W$_{b}$ = 1(10 - 5) N

W$_{b}$ = 5N

$\frac{W_{b}}{g}$= 0.5 kg

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

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.