Mass and Weight

Mass and weight are fundamental concepts in physics that help us understand how objects behave under the influence of forces, especially gravity. In everyday life, these terms are often used interchangeably, but in physics, they have distinct meanings and significance. Mass is a measure of the amount of matter and inertia in a body, whereas weight is the force acting on it due to gravity.

To understand this difference, we must consider how forces act in nature. Any change in the speed or direction of an object requires a force. For example, when an object is dropped from a height, it falls toward the Earth; planets revolve around the Sun, and the Moon revolves around the Earth. All these motions occur due to a common force identified by Isaac Newton, known as the gravitational force. Understanding mass and weight helps explain how this force affects different objects.

Mass

Mass is defined as the amount of matter present in a body. It is also a measure of a body's inertia, which means its resistance to any change in its state of rest or motion.

Mass is an intrinsic property of an object, meaning it remains constant everywhere—whether the object is on Earth, the Moon, or in outer space.

Formula of Mass (when density is known): \boxed {m = \rho V}

Key Characteristics of Mass

1. It is a scalar quantity (only magnitude, no direction).
2. It does not depend on gravity or location.
3. It can never be zero for a physical object.
4. It is measured using a beam balance or digital balance.
5. Its SI unit is kilogram (kg).

Weight

Weight is defined as the force with which a body is attracted towards the Earth or any other celestial body due to gravity. Unlike mass, weight is not constant and varies depending on the gravitational field.

Formula of Weight: \boxed { W = mg }

Key Characteristics of Weight

1. It is a vector quantity (has both magnitude and direction).
2. It always acts towards the center of the Earth or attracting body.
3. It changes with location because gravity varies.
4. It can be zero in space, where gravity is negligible.
5. It is measured using a spring balance.
6. Its SI unit is the newton (N).

Acceleration Due to Gravity (g)

Whenever an object falls freely under the influence of gravity, it experiences an acceleration called acceleration due to gravity, denoted by (g).
\boxed {g = \frac{GM}{R^2}}

where:

• G = Universal gravitational constant
• M = Mass of the Earth (or planet)
• R = Radius of the Earth (or distance from center)

On Earth, the value of (g) is approximately 9.8 m/s².

Relation Between Mass and Weight

From Newton’s second law of motion:
F = ma

For gravitational force:
W = mg

This shows that weight is directly proportional to mass, but it also depends on gravity. Hence, if gravity changes, weight changes, but mass remains constant.

Difference Between Mass and Weight

Weight on Different Celestial Bodies

The value of gravity differs from planet to planet, so weight also changes accordingly.

• On the Moon, gravity is about 1/6th of Earth’s gravity
• Therefore, weight on the Moon is:W_{\text{moon}} = \frac{1}{6} W_{\text{earth}}

This is why astronauts feel lighter on the Moon, even though their mass remains the same.

Weightlessness

Weightlessness is the condition in which a body appears to have zero weight. This occurs when there is no normal reaction force acting on the body, such as during free fall.

Examples:

• Astronauts in a space station
• A person in a freely falling elevator

In these cases, even though gravity is present, the body does not feel its weight because everything is falling together.

Examples and Applications

1. A person of mass 60 kg will have:
   W = 60 x 9.8 = 588 N (on Earth)
2. On the Moon:
   W = 60 x 1.62 = 97.2 N

This clearly shows how weight changes but mass remains constant.

Related Articles:

• Mass Formula
• Fundamental Forces
• Pulley in Physics

Solved Problems

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