Dimensions of 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