Question

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 

Answer 1

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 mass, length, 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