# Dimensions of Young Modulus

## Dimensional Formula of Young Modulus

The dimensional formula of Young Modulus is given by,

[M1 L-1 T-2]

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

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

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

⇒ Force = M × a = M × [M1 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].