Determine the dimensions for W if W = P L^3 / (M V^2) where P is a pressure, L is a length, M is a mass, and V is a velocity.

a. M
b. L / T
c. M L / T^2
d. M / (L T^2)
e. No dimensions

Answers

Answer 1

Correct answer is option E. No dimensions

As we know formula Pressure (P) is [tex]\frac{F}{A}[/tex]

also,

Dimensional formula of Pressure is [tex]M^{1}L^{-1}T^{-2}[/tex]Dimensional formula of length is L Dimensional formula of mass is MDimensional formula  of velocity is [tex]L^{1} T^{-1}[/tex]

So, as given W=[tex]\frac{P*L^{3} }{M*V^{2} }[/tex]

Dimensional formula of W =[tex]\frac{M^{1}L^{-1}T^{-2} L^{3} }{M^{1} L^{2}T^{-2} }[/tex]

since all terms get cancelled

Work is dimensionless i.e no dimensions

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