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What is the Dimensional Formula of Work?

Work is defined as force multiplied by displacement .Mathematically its formula is

Work= Force x Displacement

Now, we have already derived the dimensional formula for force and displacement. So
Dimensional Formula of Force= M1L1T-2
Dimensional Formula of Displacement = M0L1T0

Thus
Dimensional Formula of Work= (M1L1T-2) x M0L1T0

Dimensional Formula of Work= M1L2T-2
SI units of Work is Joule represented by J

It should be noted that energy of all types ( Surface Tension, Kinetic, Potential etc) have the same dimensional formula as that of Work. Moreover the Moment of Force represented by N-m also have same Dimensional formula

posted in Dimensional Formulae | 31 Comments

Derive the Dimensional Formula of Universal Constant of Gravitation?

Universal Constant of Gravitation is represented by G and is derived from Newton’s law of gravitation. Newton’s law states that
F=(Gm1m2)/r2
So
G=(Fr2)/m1m2

Where F is Force between masses m1, m2 at a distance r

Dimensional Formula of Force= M1L1T-2

Thus
Dimensional Formula of Universal Constant of Gravitation= (M1L1T-2 x L2)/(M1 x M1)

Dimensional Formula of Universal Constant of Gravitation = M-1L3T-2
SI unit of Universal Constant of Gravitation is Nm2kg-2

or

Dimensional Formula of Gravitational constant = M-1L3T-2

posted in Dimensional Formulae | 37 Comments

What is the Dimensional Formula of Pressure?

Pressure is defined as force per unit area.Mathematically its formula is

Pressure = Force/Area
Now, we have already derived the dimensional formula for force and area in previous posts. So
Dimensional Formula of Force= M1L1T-2
Dimensional Formula of Area= M0L2T0
Thus
Dimensional Formula of Pressure = (M1L1T-2)/(M0L2T0)
Dimensional Formula of Pressure = M1L-1T-2
SI unit of Pressure is  Nm-2(Nm-2 is also called as Pascal).

we can also state that SI unit of Pressure is Pascal
Note – Stress also has the same dimensional formula

posted in Dimensional Formulae | 31 Comments

What is the Dimensional Formula of Impulse?

Impulse is defined as the integral of a force with respect to time. In other words the change in momentum is called Impulse. Formula of Impulse is

Impulse = Force x Time
Now
Force = Mass x Acceleration

As derived earlier
Force = M x M0L1T-2

So Dimensional Formula of Impulse= M1L1T-1
SI unit of Impulse is Ns

posted in Dimensional Formulae | 12 Comments

What is the Dimensional Formula of Force?

Force is defined as an influence that causes a mass body to accelerate or change its velocity. Mathematically its formula is

Force = Mass x Acceleration
Acceleration = Change in Velocity/Time Taken
Acceleration = M0L1T-2

Substituting this in Force formula we get
Force = Mass x Acceleration
Force = M x  M0L1T-2

So Dimensional Formula of Force= M1L1T-2
SI unit of Force is kg ms-2 popularly known as  Newton (N)

Note – Thrust and Tension also has the same Dimensional formula as that of Force

posted in Dimensional Formulae | 30 Comments