The physical quantity with dimensions M L T^-2 (mass × length × time^-2) corresponds to which of the following?

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:

• Base dimensions used: M (mass), L (length), T (time).
• Target dimension: M L T^-2.
• Classical mechanics definitions are assumed.

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:

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