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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

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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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What is Dimensional Formula of Angle?

Angle is defined as the ratio of length of arc to radius.

Mathematically,

Angle = Length of Arc / Radius

Dimensional formula of Length = M0L1T0
Dimensional formula of Radius = M0L1T0

Substituting in the above formula we get,
Dimensional formula of Angle = M0L0T0. We can also say Angle is dimensionless quantity.
SI unit of Angle is radian (rad)

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What is Dimensional Formula of Mechanical equivalent of heat?

Mechanical equivalent of heat can be defined as the amount of work done to produce a unit quantity of heat. In other words whenever a mechanical work is completely transformed into heat, the amount of heat produced is directly proportional to the amount of work done.

W ∝ Q  —— Where W = Amount of Work and Q = units of heat.
W = J Q

In the above equation constant J is Known as Mechanical equivalent of heat or Joule’s equivalent.
From above equation we get,

Mechanical equivalent of heat (J) = Amount of Work (W) / units of Heat (Q).

Dimensional Formula of Work = M1L2T-2
Dimensional Formula of Heat = M1L2T-2

substituting these values we get,

Dimensional Formula of Mechanical equivalent of heat (J) = M0L0T-0 . we can also say Mechanical equivalent of heat (J) is dimensionless quantity.
SI unit of Mechanical equivalent of heat (J) is Joules/calorie (J calorie-1 ).

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What is the formula for Internal Energy?

Internal energy (U) is defined as the energy which is related to atomic, sub atomic and molecular energy of the system. Internal energy comprises of the kinetic and potential energy related with transitional , rotational and vibrational motion of the molecules, it also includes the energy of electromagnetic interactions of molecules , atomic and sub atomic constituents of molecules.

Mathematically,
Internal energy (U) = Energy.
Dimensional formula of Energy = M1L2T-2

So Dimensional Formula of Internal Energy (U) = M1L2T-2
SI unit of Internal Energy (U) is Joule (J)

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