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If area (A), velocity (v) and density (ρ) are taken as the fundamental units, what will be the dimensional formula for force? 


1. Av2 ρ 
2. A2 vρ 
3. Avρ2 
4. Avρ 

1 Answer

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Best answer
Correct Answer - Option 1 : Av2 ρ 

CONCEPT:

  • Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit, and a Dimension is a mathematical tool used for studying the nature of physical quantities
  • The basic concept of dimensions is that we can add or subtract only those quantities which have the same dimensions.
  • And the dimensional formula is defined as the expression of the physical quantity in terms of masslength, and time.

EXPLANATION

Given -  A = Area, V= Velocity, ρ = Density

  • Force is a quantity that changes either the state of rest or uniform motion of an object.
  • Mathematically, it is written as

⇒ F = ma

  • The dimension of force is given by

F = [ M L T-2]

  • The dimension of the first option is given by

AV2ρ = [L2] × ([LT-1])2× [ML-3]

⇒ Dimension = [ M L4× L-3 T-2]

⇒ Dimension = [ MLT-2]

  • The dimension of option 1 is equal to the dimension of force
  • Hence, option 1 is the answer

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