Mass Formula 

What is Mass?

Mass is a fundamental property of matter that measures the amount of substance an object contains. It is a scalar quantity and is typically measured in kilograms (kg) or grams (g). Mass plays a crucial role in various scientific disciplines, including physics, chemistry, and engineering.

Mass is the amount of matter that is present in the object. The mass of an object remains constant no matter where it is placed.

Suppose, we have two same objects out of which one is placed on the Earth and the other is placed on the moon. Since the matter in the object is not changing, the mass of the object will be the same in each of the cases.

The standard unit of mass is Kilogram (Kg).

The mass of an object can be calculated using the following formula:

Mass (m) = Density (ρ) × Volume (V)

This formula assumes that the density of the object is constant throughout.

So, if you know the density and volume of an object, you can calculate its mass using the formulas above.

What is Weight?

The weight of an object is the measurement of the gravitational force acting on it. It is a measure of how strongly gravity pulls on the matter.

Formula of Weight

According to Newton’s second law of motion, force is equal to the mass in acceleration,

F = m x a

When its acceleration is due to gravity, a = g

F = m x g

This force due to gravity will be equal to the weight of the object, W. So,

W= m x g

This means the weight of an object is the product of its mass and acceleration due to gravity. The SI unit of weight is Newton (N) which is the same as Force. As the value of g at a particular place is constant, the weight of the object is directly proportional to its mass.

What is the difference between Mass and Weight?

The mass of an object remains constant everywhere whereas the weight of an object depends on the gravitational force at the location.

If an object of the same mass is placed at two different places and the gravitational force at one place is more than the other, then the mass of the object will be the same at both places. But, the weight of the object will be greater at the second place because the pull of gravity is stronger.

Solved examples on Mass Formula

Example 1: Calculate the mass of an object given its density and volume.

Density (ρ) = 5 g/cm³

Volume (V) = 100 cm³

Solution:

Using the formula: Mass (m) = Density (ρ) × Volume (V)

Mass (m) = 5 g/cm³ × 100 cm³

Mass (m) = 500 g

Therefore, the mass of the object is 500 grams.

Example 2: Determine the weight of an object on Earth given its mass.

Mass (m) = 2 kg

Acceleration due to gravity (g) = 9.8 m/s²
Solution:
Using the formula: Weight (W) = Mass (m) × Acceleration due to gravity (g)
Weight (W) = 2 kg × 9.8 m/s²

Weight (W) = 19.6 N

Therefore, the weight of the object on Earth is 19.6 Newton.

Example 3: Determine the weight of a person with a mass of 70 kg on the surface of the Moon, where the acceleration due to gravity is about 1.6 m/s².

Solution:

Mass (m) = 70 kg

Acceleration due to gravity on the Moon (g) = 1.6 m/s²

Using the formula: Weight (W) = Mass (m) × Acceleration due to gravity (g)

Weight (W) = 70 kg × 1.6 m/s²

Weight (W) = 112 N

Therefore, the weight of the person on the surface of the Moon is 112 Newton.

Frequently Asked Questions on Mass Formula

What is mass?

Mass is a fundamental property of matter that measures the amount of substance an object contains. It quantifies the inertia of an object and determines its resistance to changes in motion.

How is mass different from weight?

Mass and weight are often used interchangeably in everyday language, but they have distinct meanings in physics. Mass represents the amount of matter in an object and is a scalar quantity, measured in kilograms (kg) or grams (g). Weight, on the other hand, refers to the force exerted on an object due to gravity and is a vector quantity, measured in Newton (N) or pounds (lb).

How is mass measured?

Mass can be measured using various techniques and instruments. In everyday life, smaller masses are typically measured using balances or scales, which compare the unknown mass to known reference masses. In scientific settings, mass is often measured using more precise instruments such as analytical balances or mass spectrometers.

Is mass conserved in physical processes?

According to the law of conservation of mass, mass is conserved in closed systems during physical and chemical processes. This means that the total mass of the substances involved before and after a process remains the same, even if there are changes in form or state.

What is the difference between mass and molar mass?

Mass refers to the amount of matter in an object, while molar mass is the mass of one mole of a substance. Molar mass is expressed in units such as grams per mole (g/mol) and is used to relate the mass of a substance to the number of moles it contains.

Can mass be negative?

In classical physics, mass is always positive and cannot be negative. However, in certain branches of physics, such as theoretical physics and quantum field theory, there are concepts of negative mass or exotic matter that have hypothetical properties and are not observed in everyday phenomena.

Does mass change with location or gravitational field?

The mass of an object remains the same regardless of its location or the gravitational field it is in. However, an object's weight, which is the force exerted on it due to gravity, can vary depending on the strength of the gravitational field.