Question

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

Answer 1

Correct answer is option E. No dimensions

As we know formula Pressure (P) is $\frac{F}{A}$

also,

• Dimensional formula of Pressure is $M^{1}L^{-1}T^{-2}$
• Dimensional formula of length is L
• Dimensional formula of mass is M
• Dimensional formula  of velocity is $L^{1} T^{-1}$

So, as given W=$\frac{P*L^{3} }{M*V^{2} }$

Dimensional formula of W =$\frac{M^{1}L^{-1}T^{-2} L^{3} }{M^{1} L^{2}T^{-2} }$

since all terms get cancelled

Work is dimensionless i.e no dimensions

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