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Question

Write down the units and dimensional formulae of following physical quantities:
Power=worktime


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Solution

Units and dimensional formula of power:

  • Power can be defined as the rate at which a work is done.
  • Mathematically, it can be given as Power=worktime.
  • So, the unit of power =kgm2s-2s=kgm2s-3, i.e., kilogram meter square per second cube.
  • This unit in the SI system is called Watt (W), which in simpler terms is nothing but Newton-metre per second (N-ms-1).
  • Write the formula of power in terms of fundamental quantities to find the dimensional formula:
    Power=worktime=work×(time)-1[P]=[ML2T-2]×[T-1]=[ML2T-3]

Thus, the unit of power is Watt(W),i.e.,N-ms-1orkgm2s-3 and its dimensional formula is [ML2T-3].


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