Mass and Weight

Mass and Weight are commonly used in the same manner by the general masses but there are differences between both Mass and Weight, where Mass is the measure of Inertia unlike Weight which is a measure of force acting on a body towards the heavy body. But yet still many people use these two terms interchangeably.

As we know that to change the speed or direction of an object, a force is required. If you drop anything from a great height, it will fall towards the earth’s surface. The planet revolves around the Sun and the moon revolves around the earth. There must be some force operating on objects, planets, and other celestial bodies. Isaac Newton noted that the same force is responsible for all these. This force is called gravitational force. 

What is Mass?

Mass is defined as the measure of the amount of matter present in a body. The mass of the body remains the same everywhere, irrespective of location. Thus, mass refers to both, the property of a physical body and the measure of the resistance of the object to acceleration when we apply a net force.

The inertia of an object is measured by its mass i.e. the mass of an object is the measure of its inertia. When the mass of the body increases there will be an increment in the inertia also. The mass of the body does not change with the place. Whether an object is on the Earth, the Moon, or even in space, its mass remains constant. As a result, an object’s mass is constant and does not vary with its location. 

The formula to calculate the mass of an object when its density and volume is given, is:

Mass (m) = Volume (V) × Density (ρ)

It is a scalar quantity and its SI unit is kilogram (kg).

The mass of an object is measured by using an ordinary balance, beam balance, or digital balance. The general properties of mass can be summarised as,

• Mass of anybody can never be zero.
• Mass is a scaler quantity as it only has magnitude.
• Mass of an object does not change with the change in its location.
• Common Balance is used to measure the mass of a body.
• SI unit of mass is grams (g) and kilograms (kgs).

The common balance used to measure the mass is shown in the image below,

What is Weight?

The weight of an object is defined as the measure of the amount of force that acts on mass because of the pull of gravity. Weigh is the measure of force. Therefore, Weight will vary depending on the location.

The earth attracts every item with a force that is proportional to the object’s mass (m) and acceleration due to gravity (g).  It is a vector quantity as it got the magnitude and direction toward the Earth’s center or other gravity.

The SI unit of weight is Newton, which is the same as the SI unit of force (N) and it is measured using a spring balance. A spring balance is shown in the image below.

The general properties of mass can be summarised as,

• Weight of a body can be zero if the gravity associated in any case is zero such as in the case of space.
• Weight is a vector quantity as it has both magnitude and direction.
• Weight of a body changes with the change in its location.
• Spring balance is generally used to measure weight. 
• The SI unit of weight is Newton.

Acceleration Due to Gravity (g)

Whenever an object falls toward the earth, it experiences acceleration. The earth’s gravitational force is responsible for this acceleration. This acceleration is known as acceleration due to gravity. It is denoted by g. The unit of g is m s^–2, which is the same as the unit of acceleration. The formula to calculate g is given as follows:

g = GM/R²

where, 
G is Universal Gravitational Constant (G = 6.67 × 10^-11 Nm²/Kg²)
M is the mass of the Object on which we are calculating g.
R is the radius of the Object.

Measurement of Weight

Everything is attracted to the earth with a certain force and this force depends on the mass (m) of the object and the acceleration due to gravity (g).

The Force on any object of mass m which is moving with acceleration a can be expressed as,

F = m × a

As all objects experience acceleration due to gravity on the Earth,

F = m × g

The weight of an object is defined as the earth’s force of attraction on it and it is represented by W. 

W = m × g

The weight is a downward-acting force that has both magnitude and direction so, it is a vector quantity. 

Weight on Earth

The distance between a point at the equator and the centre of the earth and the distance between the point at the North Pole and the centre of the earth.

The earth’s shape looks spherical, but it is an unevenly shaped ellipsoid. The distance between a point at the equator and the centre of the earth is more than the distance between the point at the North Pole and the centre of the earth. From the expression,

• g = GM/R²
• W = mg

It is observed that acceleration due to gravity (g) is inversely proportional to the square of the distance between the object and the earth, an object placed at the North Pole would have more weight than the weight at the equator. Therefore, as the mass remains constant but the acceleration due to gravity varies from place to place, the weight of an object can also vary from place to place on the earth’s surface.

Weight on Moon

The weight of an object on the Earth is the force with which the earth attracts the object. Similarly, the weight of an object on the moon is the force that attracts that object to the moon. The moon has a mass that is less than that of the Earth. As a result, the moon has less attraction to objects i.e., approximately (1/6)^th of the Earth’s force of attraction. Thus weight on the moon is (1/6)^th of the weight on Earth.

Difference Between Mass and Weight

The difference between the mass and the weight are as follows,

Mass	Weight
The mass of an object can never be zero.	When there is no gravity acting on an item, such as  in space, weight can be zero.
The mass is a property of matter. An object’s mass is  constant everywhere.	The effect of gravity has an impact on weight. With  higher or lower gravity, weight increases or decreases.
Mass is a scalar quantity. It has only magnitude, not  direction.	Weight is a vector quantity. It has both magnitudes as  well as direction.
Mass is commonly measured in kilograms (kg) and  grams (g).	Weight is measured in Newtons (N).
The mass of an object does not change with its position.	The weight of an object change with its position.
The mass of an object is measured by using an ordinary  balance.	The weight of an object is measured by using a spring  balance.

Weightlessness

The phenomenon when an object’s effective weight becomes zero is known as weightlessness. For example, astronauts in the space station orbiting around the Earth experience the condition of weightlessness and float freely inside the station. Other than this, some more examples include passengers on board an aeroplane, people inside a free-falling elevator, divers and swimmers (due to the buoyancy of water) who can also feel the same, etc.

Learn more about, Weightlessness

Sample Problems on Mass and Weight

Problem 1: The Mass of an object is 10 kg. What is its weight on the earth?

Solution:

Given that, 

Mass (m) = 10 kg

Acceleration due to gravity (g) = 9.8 m s^–2

Expression of the weight is 

W = m × g

Substitute the values in the above equation.

W = 10 kg × 9.8 m s^-2 = 98 N

Thus, the weight of the object is 98 N.

Problem 2: An object weighs 10 N when measured on the surface of the earth. What would be its weight when measured on the surface of the moon?

Solution:

Given,

Weight of an object on Earth is 10 N

Relation between the weight of an object on Earth (W_e)  and weight of an object on Moon (W_m)

W_m = (1⁄6)×W_e

Substitute the value in the above expression.

 W_m = (1⁄6)×10 N

 W_m = 1.67 N

Thus, the weight of the object on the surface of the moon would be 1.67 N.

Problem 3: What is the relation between the weight of an object on the Earth and the weight of an object on the moon?

Solution:

Given,

• Mass of the Earth is 5.98 ×10²⁴ kg.
• Mass of the Moon is 7.36×10²² kg.
• Radius of the Earth is 6.37×10⁶ m.
• Radius of the Moon is 1.74×10⁶ m.

Let the mass of an object be m, the weight on the moon be W_m, the mass of the moon be M_m and its radius be R_m.

From the universal law of gravitation,

W_m = (G M_m m)/(R)²

Substitute the values in the above expression.

W_m = (G 7.36×1022 kg m)/(1.74×10⁶ m)² . . .(1)        

Let the weight of the same object on the earth be W_e, the mass of Earth is M and its radius is R then the expression for the weight of the object on Earth is

W_e = (G M m)/(R)²

Substitute the values in the above expression

W_e = (5.98 ×1024 kg m)/(6.37×10⁶ m)². . .(2)

Divide equation (1) and (2),

W_m/W_e = 2.431 1010/1.474 1011

⇒ W_m/W_e = 0.165

⇒ W_m/W_e ≈ 1/6

⇒ W_m ≈ (1⁄6)×W_e

FAQs on Mass and Weight

Q1: What is the difference between Mass and Weight?

Answer:

Mass is the measure of Inertia unlike Weight which is measure of force acting on a body towards the heavy body. Commonly people use both the terms in the same manner but there are a lot of differences between both which is well explained in the article above.

Q2: What is the SI unit of Mass?

Answer:

Kilogram is the SI unit of Mass, and other units of mass include gram, pound, ton etc.

Q3: What is the SI unit of Weight?

Answer:

SI unit of Weight is Newton (N) which is also written as Kgm/s². Other units of weight is dyne(CGS system).

Q4: What is Mass of an Object?

Answer:

Mass of an object is defined as the measure of all the substance that are present inside the body. Mass of any object is measured in kg. The mass of any object does not change with the change in the gravity.

Q5: What is Weight of an Object?

Answer:

Weight of an object is defined as the gravitational force exerted by a body on the surface of the planet. The weight of any object on Earth is the force exerted by an object on the surface of the Earth. It is measured in Newtons.