Difficulty: Easy
Correct Answer: Force
Explanation:
Introduction / Context:Dimensional analysis helps engineers check equations, scale models, and identify governing non-dimensional parameters. Recognizing the base dimensions behind a symbol prevents unit mistakes in design and exams.
Given Data / Assumptions:
Concept / Approach:
From Newton’s second law, force F = m * a. Dimensions: [m] = M, [a] = L T^-2, so [F] = M L T^-2. Compare with other listed quantities to ensure no ambiguity.
Step-by-Step Solution:
Write dimensions of force: M L T^-2.Specific weight γ = weight/volume = (M L T^-2)/L^3 = M L^-2 T^-2.Discharge Q = volume/time = L^3 T^-1.Dynamic viscosity μ = shear stress / velocity gradient = (M L^-1 T^-2)/(T^-1) = M L^-1 T^-1.Verification / Alternative check:
Check units in SI: Force in newtons (N) = kg·m/s^2, which maps directly to M L T^-2.
Why Other Options Are Wrong:
(a) Specific weight includes L^-2, not L^1. (c) Discharge lacks M. (e) Dynamic viscosity includes L^-1 T^-1, not L T^-2. (d) is unnecessary since a correct match exists.
Common Pitfalls:
Mixing specific weight with pressure dimensions, or confusing dynamic viscosity with kinematic viscosity (which is L^2 T^-1).
Final Answer:
Force
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