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Difference Between Mass and Weight

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Last updated date: 14th Apr 2024
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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

Context

Mass

Weight

Defining Property

When a force is applied to an object, the amount of acceleration it experiences determines its mass.

Any object with mass experiences gravitational force in a gravitational environment. The weight of the object is the gravitational force.

Quantity Type

Mass is a fundamental or base quantity

Weight is a derived quantity.

Dimension

[M]

[MLT-2] weight has a dimension of force.

Physical Quantity Type (scalar or vector)

Because it only has magnitude and no direction, Mass is a scalar quantity.

Weight is a vector quantity.

Units

SI unit: kilogram (kg)

CGS unit: gram (g)

FPS unit: pound (lb)

SI unit: kgms-2 or Newton

Represented by (N)

CGS unit: gcms-2 or dyne

Represented by (Dyn)

FPS unit: lbfts-2 or poundal

Represented by (pdl)

Effect of Gravity

Because mass is an inherent feature, gravity does not affect it. A physical body's mass remains constant if it does not release or absorb energy in any manner.

Weight fluctuates with the gravitational field because it is related to gravitational acceleration.

Zero Gravity Condition

A body's mass is not zero when it is not in a gravitational field.

Weight is zero in a gravitational region with zero gravity. During an ideal free fall or in space, for example, a person's weight is practically nil.

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. 

Presence of Forces other than gravity

The definition of mass is that it is independent of all forces.

As a result, it remains unchanged in the presence of forces.

When an object is subjected to varied forces, its weight varies.

Consider the case below:

  • Buoyant force occurs when a body is submerged in a fluid. As a result of this force, the weight of the immersed body changes.

  • The weight of a person can shift inside an accelerating lift. If the acceleration is upwards, it becomes heavier, and if it is downhill, it becomes lighter.

 

  • The body effectively becomes weightless during a free fall (downward acceleration equal to gravitational acceleration).  


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.

FAQs on Difference Between Mass and Weight

1. What are mass and weight?

Mass of an object is a measure of the amount of matter in it and also its inertia. Any physical object resists a change in its state of motion. This resistance is due to mass, which is an intrinsic property. Weight is the force acting on a massive object due to a gravitational field.

2. What is the difference between mass and weight? Give an example.

Weight is proportional to mass but they are fundamentally different. Mass is a scalar quantity that does not change. Weight is a vector and it changes under the change of gravitational acceleration. The mass of a physical object can never be zero although its weight can. An object weighs differently on the Earth and the Moon but its mass remains the same. For example, the weight of an object of mass 120 kg is 1200 N on the Earth. However, its weight on the Moon is 200 N.

3. Is mass production a viable option?

The principle of mass conservation, also known as the law of conservation of mass, states that the mass of any system closed to all transfers of matter and energy must remain constant over time because the mass of any system closed to all transfers of matter and energy cannot change and thus quantity cannot be added or removed.

4. Is it possible for a body to have mass but not weight?

W=MG, where m denotes mass, g denotes gravitational acceleration, and w denotes a body's weight. G is solely determined by a planet's gravitational attraction, which is determined by the mass of the planet at a certain position. Because the acceleration due to gravity at the Earth's center is zero, we can write W = Mx0. So, even though a body has mass, its weight can be zero.

5. What is weightlessness?

Weightlessness is a state of free fall in which gravity's effect is cancelled by the inertial (e.g., centrifugal) force generated by orbital flight. The objects are not subjected to gravitational attraction. It's a condition in which the body can't detect its own weight. When an apple falls from a tree, it does not feel the weight of its fall. Weightlessness is a state that anyone in free fall can achieve.

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The most tempting feature of this app is that it offers free study materials related to the topic Mass & Weight to students and subscribers. As part of the Vedantu Packages, NCERT Solutions, Previous Year Question Papers, Important Questions, and other PDF material are all accessible for free download. To get your kids ready for their examinations, use the free study material feature of the unique Vedantu app download.