Question

What is the dimensional formula of Modulus of Elasticity?
1. M1L0T2. M¹L^-1T^-2
3. ML-1T-2
4. M¹L¹T^-1

Answer 1

Correct Answer - Option 2 : M¹L^-1T^-2

Option 2 is correct, i.e. M1L-1T-2.

•  Modulus of Elasticity:
  • Scientist Hooke has given a law regarding this. The law is "Under elastic limit, stress is proportional to strain".
  • As per this law, we get the Elastic constant or modulus of elasticity and it is denoted by the symbol E.
  • The value of this modulus of elasticity is different for different materials.
  • The SI unit of this is Nm^-2 or Pascal. 

We know that young’s modulus or modulus of elasticity e = stress/strain

⇒ Stress unit is N/m² and strain has no units

Dimensional formula for stress = [ML^-1T^-2]

⇒ young’s modulus = stress/strain = [ML^-1T^-2]/ [M⁰L⁰T⁰] = [ML^-1T^-2]

∴ Dimensional formula of young’s modulus = [ML^-1T^-2]

Elasticity constant is of three types: 

Elasticity constant name	Symbol	Formula
Young's modulus	Y	Longitudinal stress/Longitudinal strain
Bulk Modulus	K	Volume stress/Volume strain
Rigidity modulus	G	Tangential stress/ Tangential strain