Classical units: one “metric slug” (hyl) is numerically equal to what quantity?

Introduction / Context:
Older engineering literature sometimes uses the term “metric slug” (also known as the hyl) as an analogue to the imperial “slug.” Understanding these legacy mass units helps interpret historic design tables and exam questions that mix gravitational and absolute unit systems.

Given Data / Assumptions:

• Standard gravity g_0 ≈ 9.81 m/s^2.
• 1 kilogram-force (kgf) is the weight of 1 kg mass under g_0.
• “Metric slug” (hyl) is defined such that a force of 1 kgf produces an acceleration of 1 m/s^2 on it.

Concept / Approach:

From F = m * a, set F = 1 kgf and a = 1 m/s^2. But 1 kgf = 9.81 N. Therefore the mass m satisfying 9.81 N = m * 1 m/s^2 is m = 9.81 kg. Hence, one metric slug equals approximately 9.81 kilograms of mass, not kilogram-force (a force unit).

Step-by-Step Solution:

Verification / Alternative check:

Compare with the imperial slug where 1 slug * 1 ft/s^2 = 1 lbf, yielding 1 slug ≈ 32.174 lbm. The analogy confirms the concept of defining mass via a chosen gravitational force unit and unit acceleration.

Why Other Options Are Wrong:

(a), (b), and (d) are weights (forces) expressed in kgf, not masses. (e) confuses the distinct imperial unit “slug” with the “metric slug”; they are not numerically equal.

Common Pitfalls:

Mixing mass and force units; overlooking that “kg wt” refers to kgf (a force), while the question asks for mass equivalence.

Final Answer:

9.81 kg mass