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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

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

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

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

What is the Dimensional Formula of Acceleration?

Acceleration is defined as change in velocity per unit time. So its formula is
Acceleration = Change in Velocity/Time Taken

Now
Velocity = Displacement/Time
Velocity = L/T
So
Acceleration = L/T2

So Dimensional Formula of Acceleration= M0L1T-2
SI unit of Acceleration is ms-2

The Dimensional Formula of Acceleration due to gravity (g) is also same as acceleration.