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

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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

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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