Dimensional analysis—dimensions of force in MLT system What is the correct dimensional formula for force (Newton’s second law) in terms of mass M, length L, and time T?
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AMLT-2
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BM-1LT2
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CML-2T
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DM-1L2T-2
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Enone of these.
Answer
Correct Answer: MLT-2
Explanation
Introduction / Context:Dimensional homogeneity is the backbone of fluid mechanics and all of engineering analysis. Identifying the correct dimensions of fundamental quantities helps in validating equations and building non-dimensional groups (e.g., Reynolds, Froude, Weber numbers).
Given Data / Assumptions:
- Force F is related to mass m and acceleration a by F = m * a.
- Base dimensions: mass M, length L, and time T.
Concept / Approach:
Acceleration a has dimensions of length per time squared, and mass is simply M. Multiplying these gives the well-known MLT^-2 for force. This is consistent with SI, where the Newton (N) is kg·m/s^2.
Step-by-Step Solution:
Acceleration a → L T^-2.Mass m → M.Force F = m a → M * (L T^-2) = M L T^-2.Verification / Alternative check:
Energy (work) W = F * L gives dimensions M L^2 T^-2, consistent with Joule, further validating F = M L T^-2.
Why Other Options Are Wrong:
(b), (c), and (d) mismatch exponents; (e) is unnecessary since a correct option exists.
Common Pitfalls:
Dropping negative signs on time exponents; confusing derived units (N) with base dimensions; mixing CGS and SI inconsistently.
Final Answer:
MLT-2