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What is Dimensional Formula of Gravitational Potential Energy?

The Gravitational Potential Energy of a body at a point in a gravitational field is defined as the amount of work done in bringing the body from infinity to that point without acceleration.The gravitational potential energy at a point is always negative.

Mathematically,

Gravitational Potential Energy  = Gravitational Potential X mass of body (m).

Dimensional formula of Gravitational Potential = M0L2T-2
Dimensional formula of Mass = M1L0T0

Putting these values in above equation we get,

The Dimensional formula of Gravitational Potential Energy is M1L2T-2.
The SI unit of Gravitational Potential Energy is Joule (J).

What is the dimensional formula of Gravitational Field Intensity or Gravitational Strength?

Gravitational Field Intensity or Gravitational Strength at a point is defined as the gravitational force exerted on a unit mass placed at that point.

Mathematically,

Gravitational Field Intensity or Gravitational Strength = GM /r2
where G = Gravitational Constant, M = mass and r = distance from the centre of the body to the point.

Dimensional Formula of Universal Constant of Gravitation = M-1L3T-2
Dimensional Formula of Mass = M1L0T0
Dimensional Formula of Radius = M0L1T0

Substituting in the above equation we get,
Dimensional Formula of Gravitational Field Intensity or Gravitational Strength = M0L1T-2
SI unit of Gravitational Field Intensity or Gravitational Strength is N kg-1 or it can also be written as m s-1

Note: Gravitational Field Intensity is often referred as Gravitational Field.

What is the Dimensional Formula of Spring Constant?

Spring Constant is defined as restoring force per unit displacement. Force is directly proportional to the displacement of the system. It can also be stated as force needed to compress or extend a spring is directly proportional to the displacement of the spring.

Mathematically,

Spring Constant = Force/Displacement

Dimensional Formula of Force = M1L1T-2
Dimensional Formula of Displacement = M0L1T0

So Dimensional Formula of Spring Constant = M1L0T-2
SI unit of Spring Constant is Nm-1

What is Dimensional Formula of Tensile Modulus , Modulus of Elasticity, Young modulus?

Tensile Modulus , Modulus of Elasticity, Young modulus is defined as the stress required to cause a unit strain in the material. It is the ratio of linear stress to linear strain.

Mathematically,

Tensile Modulus , Modulus of Elasticity, Young modulus = linear stress / linear strain.

Dimensional Formula of linear stress = M1L-1T-2
Dimensional Formula of linear strain = M0L0T0

Substituting in the above equation we get,

Dimensional Formula of Tensile Modulus , Modulus of Elasticity, Young modulus = M1L-1T-2
SI unit of Tensile Modulus , Modulus of Elasticity, Young modulus = N m-2

What is Dimensional Formula of Poisson’s ratio?

Poisson’s Ratio is defined as the ratio of lateral contraction to linear elongation . It can also be defined as the ratio of unit transverse (Lateral) strain to unit longitudinal strain.

Mathematically,
Poisson’s ratio (σ) = Lateral Strain / longitudinal strain.

Since we have different form of strain in the above equation and Dimensional Formula of Strain = M0L0T0.

And we know that ratio of dimensionless quantity is Dimensionless.

Therefore, Poisson’s ratio is Dimensionless and has no SI unit.

 

 

 

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