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Question

Write down the units and dimensional formulae of following physical quantities:
Young'smodulus=stressstrain


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Solution

Units and dimensional formula of Young's modulus of elasticity:

  • Young's modulus of elasticity can be defined as the ratio of stress and strain.
  • Mathematically, it can be given as Young'smodulus=stressstrain.
  • So, the unit of Young's modulus =Nm-2, i.e., Newton per metre square which is nothing but Pascal (Pa) in SI system of units.
  • Its unit is the same as that of stress as strain does not have any units.
  • Use its unit to find the dimensional formula of stress:
    Young'smodulus=N×m-2[E]=[MLT-2]×[L-2]=[ML1-2T-2]=[ML-1T-2]

Thus, the unit of Young's modulus of elasticity is Pascal(Pa),i.e.,Newtonpermetresquare(Nm-2) and its dimensional formula is [ML-1T-2].


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