Unit of Weight is Newton represented as N, which is also known as the force of gravity on a mass. Weight of the body is the gravitational force by which the earth or any other planet attracts the body. Other weight units are pound-force, metric ton, slug, quintal, kilogram-force (kgf) and dyne.
In this article, we will discuss the definition of weight, unit of weight, conversion between the unit of weight in various systems, and some sample problems related to the unit of weight.
Definition of Weight
Weight of a body is defined as follows,
Weight of a body is the gravitational force by which it is attracted towards a planet.
Weight of a body is often confused with the body’s mass, which measures the amount of matter contained in a body. However, the body’s weight is the body mass multiplied by the acceleration due to gravity on the planet.
The weight of a body is different on different planets due to different values of acceleration due to gravity on various planets. For Earth, acceleration due to gravity is taken as 9.8 ms-2.
Weight Formula
The formula for weight is written as follows,
W = mg
where,
W = weight of the body,
m = mass of the body, and
g = acceleration due to gravity.
What is Unit of Weight?
Unit of Weight is the measurement of magnitude of weight according to defined standards or convention. As mentioned above, the formula for weight is mass multiplied by acceleration due to gravity. Thus, it gives the base unit of weight as kgms-2 as unit of mass is kg and that of acceleration is ms-2.
Also, we know that weight is a type of force which implies that SI unit of weight is Newton, i.e. N. Some other commonly used units of weight are kilogram-force (kgf) and dyne.
Dimensional Formula of Weight
The dimensional formula for weight is [M1 L1 T-2]. It can be derived using the formula of weight as follows.
Weight = (Mass) × (Acceleration due to Gravity)
Substituting the dimensional formula of mass and acceleration we get,
Dimension of Weight = [M1 L0 T0] x [M0 L1 T-2]
Dimension of Weight = [M1 L1 T-2]
SI Unit of Weight
SI Unit of Weight is the Newton (N). The base unit is kgms-2 which is derived as follows:
- SI unit of Mass: kg
- SI unit of Acceleration: ms-2
As, Weight = Mass x Acceleration, we get,
SI unit of Weight = (SI unit of Mass) x (SI unit of Acceleration) = kgms-2
As per SI convention, the obtained unit i.e kgms-2 is unit of force which is named after the Scientist Sir Issac Newton as Newton. Thus, SI unit of weight is Newton (N).
Unit of Weight in Other Systems
The unit of weight in different systems is written as follows:
- MKS/SI System: kgms-2 or Newton (N)
- CGS System: dyne
- Other: Pound, Metric ton, Qunital, kilogram-force (kgf)
What is 1 Newton?
1 Newton is the force required to produce an acceleration of 1 ms-2 in a body of mass 1 kg.
CGS Unit of Weight
C.G.S. system of units stands for Centimeters (length), Grams (mass), and Seconds (time). Weight of any body is the gravitational force experienced by the body on surface of the planet.
Unit of weight in CGS system is dyne. 1 dyne is equivalent to 10-5 N.
One dyne is defined as the force required to accelerate a mass of one gram at a rate of one centimeter per second squared. It is used when we need precise measurement of small weights.
SI Unit of Molecular Weight
Molecular weight is the sum of atomic masses of atoms present in one mole of a molecule. It is also known as molar mass. Molar mass is generally defined as the mass of one mole of a substance.
The SI unit of molecular weight is grams/mole. Thus, it helps us to know mass of one mole of the molecule in grams. For example, molecular weight of water (H2O) is 18 grams/mole as it is made up of two hydrogen atoms having atomic mass as 1 gram each and one oxygen atom having atomic mass as 16 grams.
Conversion Between Unit of Weight in Different Systems
The unit of weight can be converted from one system to another using following relations:
- 1 dyne = 10-5 N
- 1 pound-force = 4.448 N
- 1 kgf = 9.8 N
- 1 metric ton = 9806.65 N
- 1 quintal = 980 N
Below is a table showing the conversion factors to be used for conversion from one unit of weight to another.
|
From/To |
Newton |
dyne |
Pound Force |
kgf |
Metric ton |
Quintal |
|---|---|---|---|---|---|---|
|
Newton |
1 |
105 |
0.2248 |
0.1020 |
0.0001 |
0.001 |
|
dyne |
10-5 |
1 |
2.24 × 10-6 |
1.02 × 10-6 |
1.019 × 10-9 |
1.019 × 10-8 |
|
Pound Force |
4.448 |
444822.16 |
1 |
0.454 |
1/2205 |
1/220.5 |
|
kgf |
9.8 |
980000 |
2.205 |
1 |
1/1000 |
1/100 |
|
Metric ton |
9800 |
980000000 |
2205 |
1000 |
1 |
10 |
|
Quintal |
980 |
98000000 |
220.5 |
100 |
0.1 |
1 |
Difference Between Mass and Weight
|
Mass |
Weight |
|---|---|
|
Mass of a body is the amount of matter contained in it. |
Weight of a body is the gravitational force experienced by it on surface of the planet. |
|
Mass of a body remains constant irrespective of its location. |
Weight of a body can be different at different locations depending upon gravity. |
|
The SI unit of mass is Kilogram (kg). |
The SI unit of weight is Newton (N). |
Read More,
Solved Examples on Unit of Weight
Example 1: The weight of a body is 700 N in SI units. Find its weight in CGS units.
Solution:
We know that,
1 N = 105 dyne
700 N = 700 × 105 dyne
700 N = 7 × 107 dyne
Thus, we get weight in CGS units is found to be 7 x 107 dyne.
Example 2: The mass of a man is 40 kg. Find its weight on earth.
Solution:
Given, Mass (m) = 40 kg
We know that, Acceleration due to gravity on earth (g) = 9.8 ms-2
And, Weight (W) = mg = 40 × 9.8 = 392 N
Thus, weight of the man on earth is found to be 392 N.
Practice Problems on Unit of Weight
Problem 1: Convert 45 N into dyne.
Problem 2: Find the ratio of weight of a body on earth to that on moon. Given that, acceleration due to gravity on earth = 9.8 ms-2 and acceleration due to gravity on moon = 1.6 ms-2.
Problem 3: The weight of an object is 49 N on earth. What would be its weight on moon?
Problem 4: Mass of a body is 32 grams. Find its weight in CGS as well as SI units.
Problem 5: Convert 30 kgf weight into SI units.
FAQs on Unit of Weight
What is difference between mass and weight of a body?
Mass of a body is the amount of matter contained in it whereas Weight represents the force by which a body is attracted towards a planet.
What is formula to find weight of a body?
The weight of a body can be found using following formula,
Weight = (Mass) × (Acceleration due to Gravity)
What is SI unit of weight?
SI unit of weight is Newton (N).
What is CGS unit of weight?
CGS unit of weight is dyne.