# Dimensions of Force

## What is Force?

Force is the interaction between the bodies that occur by the cause of its change of state. It means the Force is capable of changing the state of motion of a body (example: from a body at a rest position to a body under Acceleration). Hence, we can describe the Force as an agent that brings about change in the state of motion or sometimes deformation of the shape of the body.

Before Newton, many concepts were arising regarding Force. Today, we use only the concept of Force, introduced by Newton.

Here, Newton said that “The Net Force acting upon a body is equal to its momentum rate changed over time.” Now, we use the modified version of this statement as “ The Acceleration of an object as produced by a net Force is always directly proportional to the magnitude of the net Force, present in the same direction as the net Force is inversely proportional to the object’s mass.” As we know, this statement is derived by the name Newton’s Second Law of Motion.

### Formula of Force

As described in the second law, Acceleration is the net Force divided by the total mass. Hence the net Force is net Acceleration times of total mass. It can be expressed as follows.Fnet=anetm,  where

• a is the net Acceleration of the body by which it is moving

• F is the Net Force that acts on the body

• m is the total mass of the body

The Force has the formula as below.

$F_{net} = \frac{\text{d}p}{\text{d}t} = \frac{\text m\times{d}v}{\text{d}t}$

Where,

• dt is the change in time, i.e., rate

• dp is the change in momentum of the body

• dv is the change in velocity of the body

As the momentum of the body is mass × velocity, we got the formula of Force as the rate of change of momentum.

### Dimensional Formula of Force

From the formula, stated above, we can see that Force is the mass times Acceleration.We have the unit of mass as Kg and dimensions are  [M1] [L0] [T0]  unit of Acceleration is m/s2  and expressed dimensionally as  [M0] [L1] [T−2], hence, we have the unit of Force as  Kg×m/s2So, it can be written dimensionally

As,

$\frac{[M^{1}][L^{0}][T^{0}]\times[M^{0}][L^{1}][T^{0}]}{[M^{0}][L^{0}][T^{2}]}$

$= \frac{Kg\times m}{s^{2}}$

Hence, we get the dimensional formula for Force as [M1][L1][T−2].

### Derivation of The Dimensional Formula of Force

As we know that, Force = Mass × Acceleration ---- (1)

Because, Acceleration = velocity × time–1 = [LT-1] × T-1

Thus, the dimensional formula of Acceleration is = [LT-2] ---- (2)

On substituting the equation (2) in equation (1), we get,

Force = m × a

Or, F = M × [L1 T-2] = M1 L1 T-2.

This is also called the dimensional equation of Force or the Force dimension formula.Therefore, the Force is represented dimensionally as M1 L1 T-2.

### Dimensions of Force

As we all know that, the formula of Force can be given as, F=ma

Force equals the mass times Acceleration.

And the dimension of mass is mass.

The dimension of Acceleration can be shown as velocity per time. Velocity can be shown as the distance per time.

Therefore, Mass, Time Distance, are easy to measure for us, so these are the basic dimensions we like to use.

Then, the dimension of Force is Mass, Time, Distance per Time.

The other measurement systems like to say that Force is the basic measurement, and that mass is derived from the Force.

### Why is a Gravitational Force Always Towards the Center?

A Force that purely depends only on the distance from the source has spherical symmetry. It means it will be the same on the surface of the sphere with that distance being the radius. As various bodies get attracted by the likewise Force, they will fall towards the center directly and equilibrate, if not they will be obstructed by the other Forces (including their structural integrity), into a spherical shape.

One Force, which is non-radial direction-dependent is that of a magnetic field on a charged particle in motion. The same particle will follow a fixed helical path in general with the field direction (the plane of rotation, which is perpendicular to the field), never to move towards or away from the center.

A central Force is a type of Force that points from the particle towards (away from) a fixed point the center directly, in space, and whose magnitude depends only on the distance of the object to the center.

Consider the central Force which acts along the line joining the object to the center. The representation can be given as follows.

Dimensions of Force is a part of Physics that is taught briefly in Class 11 Physics, in the NCERT book,  Chapter 2 called units and measurement. This Chapter is extremely important as it is prescribed by the Central Board of secondary education. Students who aspire to go into the medical or engineering fields have to study these concepts in-depth as the basic foundation for clearing NEET or JEE is learning and understanding the concepts taught in Class 11 and 12th NCERT books of Physics, chemistry, and biology.

JEE or the joint entrance examination is an engineering based entrance examination that is conducted every year in India. Students who aspire to create a career in the engineering field have to give a joint entrance examination JEE in order to get admission into the most reputed engineering colleges in India. The joint entrance examination or JEE is conducted by the national testing agency or NTA. The joint entrance examination is divided into JEE Main and the JEE advanced. Students get admission into IIT, NIT, IIT, and other GFTIs according to the rank that they obtain in the JEE Main and JEE advanced exams. The admission process or the seat allocation process is conducted by the joint seat allocation authority JoSAA. There are some engineering colleges that give admission based on the rank obtained in JEE advanced examination, these colleges are- IISER, IIPE, RGIPT, IIST, IISC.

Dimensions of Force is a part of Physics that is explained briefly in the NCERT books students were wanting to get a clear understanding of the topic can refer to the study notes provided by Vedantu’s team, these notes are curated according to the needs of the students as the complex concept of dimensions of Force is explained in an extremely simplified language. These notes are written by Vedantu’s expert teachers Who have done thorough research in the making of these study notes.

Students preparing for JEE Who want to get admission into reputed engineering colleges can go through the study notes provided by Vedantu as these notes will help them to get a clear understanding of the basic concepts and as the study notes are available for free they can visit Vedantu’s website and download the material in a PDF format.

The nature of any physical quantity is portrayed by its dimensions. There are a combination of seven fundamentals also known as base quantities which express the physical quantities that are represented by derived units. These quantities are referred to as the seven dimensions of the physical world, these dimensions are denoted with square blocks [ ], length [L], mass [M], time [T], electric current [A], luminous intensity [cd] thermodynamic temperature [K], and amount of substance [mol].

### Key Concepts Needed  to Understand Dimensions of Force-

• The international system of units

• Measurement of length

• Measurement of mass

• Measurement of time

• Accuracy, precision of instruments and errors in measurement

• Significant figures

• Dimensions of physical quantities

• Dimensional formulae and dimensional equations

• Dimensional analysis and its applications

## FAQs on Dimensions of Force

1. Explain the Ratio of Dimensions of Impulsive Force to the Gravitational Force.

The idea behind standard units of measure depending on the conceptual categories (like ‘Force’) is that dimensions and units within any such category are uniformed. Consequently, the units or dimensions of any Force are the same, and the ratio is unity.

Besides, any Force, whether Gravitational, magnetic, or electrical, can be/contribute to an impulsive Force. Therefore, within Newtonian mechanics, at least, all Forces, being additive, have the same units.

However, if it is something outside of Newtonian Physics, the situation could be taken as different. The problem is that, in Einstein's Gravitational theory, the General Theory of Relativity, there exists no "Gravitational Force." In this theory, gravity affects space-time, which then affects the trajectories with no need for the concept, Force.

2. Which is the Greater Force on the Gravitational and Magnetic Force?

Gravity is considered to be a weaker Force to that of electromagnetism (EM). However, the amount of exerted Force in a given circumstance will depend on the amount of mass and/or electric charge that is possessed by the interacting bodies.

Consider the Earth-Moon system. Both these are made of atoms which have mass and charge, but on each, there are EQUAL AMOUNTS of a positive and negative charge. So, the net EM Force results in zero (within our ability to measure). Whereas all mass attracts all other masses, and so gravity is the dominant Force in between the two bodies.

A hydrogen atom (OTOH) has a single proton and electron. Each of these particles has both mass and (opposite sign) charges. In such a case, the EM Force of attraction is about 1040 (i.e., crores and crores) times as strong as the Gravitational attraction.

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3. What is the formula of Force?

As studied in the second law of motion, Net Force is equal to mass multiplied by Acceleration of a particular object. This equation also gives us that Acceleration is equal to net Force divided by total mass of the particular object.It can be expressed as follows.

Fnet=anetm

where

a = net Acceleration of an object,

F = net Force acting on an object,

m = total mass of an object,

The Force has the formula as below.

Fnet = dp/dt =  m×dv/dt

4. What is the dimensional formula of Force?

We have the unit of mass as Kg and dimensions are  [M1] [L0] [T0]  unit of Acceleration is m/s2  and expressed dimensionally as  [M0] [L1] [T−2], hence, we have the unit of Force as  Kg×m/s2

So, it can be written dimensionally as,

[M1][L0][T0]×[M0][L1][T0]/[M0][L0][T2] =Kg×m/s2

Hence, we get the dimensional formula for Force as [M1][L1][T−2]

5. Explain the Ratio of Dimensions of Impulsive Force to the Gravitational Force.

The idea behind standard units of measure depending on the conceptual categories (like ‘Force’) is that dimensions and units within any such category are uniformed. Consequently, the units or dimensions of any Force are the same, and the ratio is unity.

Besides, any Force, whether Gravitational, magnetic, or electrical, can be/contribute to an impulsive Force. Therefore, within Newtonian mechanics, at least, all Forces, being additive, have the same units.

However, if it is something outside of Newtonian Physics, the situation could be taken as different. The problem is that, in Einstein's Gravitational theory, the General Theory of Relativity, there exists no "Gravitational Force." In this theory, gravity affects space-time, which then affects the trajectories with no need for the concept, Force.

6. What is Force in relation to dimension of Force?

Force in relation to dimensions of Force can be defined as the interaction that takes place between the bodies that happens because of its change of state. In other words, the Force can change the state of motion of a particular body or an object. Henceforth can be seen as an agent that brings a change in the state of motion or in some cases deforms The shape of the body. This concept was introduced by Newton and this is the only valid concept of Force. To further understand this topic students can refer to the study material provided on Vedanta’s website about dimensions of Force which includes many topics related to dimensions of Force such as formula of Force, dimensional formula Force, derivation of the formula.

7. Where can I find the study material related to dimensions of Force?

Study material related to dimensions of Force can be accessed by visiting Vedantu’s website. This study material is available in PDF format and can be downloaded for free. The PDF format helps students to download it and use it in an offline environment which is needed for better concentration. The main objective of preparing these study notes is to help students get a clearer understanding of the basic concepts of Physics and these notes include practice questions along with their solutions which can help students to ace the examination.

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