Question

If area (A), velocity (V) and density (p) are taken as fundamental units, what is the dimensional formula for force?

Options

• [AV²ρ]

• [A²Vρ]

• [AVρ²]

• [AVρ]

Answer 1

[AV²ρ]

Explanation:

F = A^αV^βρ^γ 

or [MLT^-2] = [L²]^α [LT^-1]^β [ML^-3]^γ 

`= ["M"^gamma "L"^(2alpha + beta - 3gamma)"T"^(-beta)]`

This gives : γ = 1, β = 2, 2α + β - 3γ = 1

or α = 1; F = [AV²ρ]