Young’s Modulus is usually determined by

Tensile strain ÷ tensile stress

Tensile strain × tensile stress

$$Tensile strain + tensile stress$$

$$Tensile strain - tensile stress$$

What is Dimensional Formula of Young Modulus and its Derivation?

The dimensional formula of Young Modulus is given by,

[M¹ L^-1 T^-2]

Where,

Young’s Modulus (Y) = Linear Stress × [Linear Strain]^-1. . . . . (1)

Since, linear stress = Force × Area^-1 . . . . . . (2)

⇒ Force = M × a = M × [M⁰ L¹ T^-2] . . . . (3)

⇒ Area = m² = [M⁰ L² T⁰] . . . . (4)

From equation (2), (3), and (4) we get,

The dimensional formula of linear stress = [M¹ L^-1 T^-2] . . . . (5)

And, linear strain = Change in length × [Original length]^-1= Dimension Less

On substituting equation (5) in equation (1) we get,

Young’s Modulus = Linear Stress × [Linear Strain]^-1

Or, Y = [M¹ L^-1 T^-2]

Therefore, momentum is dimensionally represented as [M¹ L^-1 T^-2].

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