Select the correct set of conversion statements relating newton, kilogram-force, pressure in kgf/cm^2, and standard atmosphere (atm) to their S.I. equivalents.

Difficulty: Easy

Correct Answer: All the above.

Explanation:


Introduction / Context:
Engineering calculations frequently involve converting between historical gravitational units (kgf, kgf/cm^2) and S.I. units (N, kN/m^2, Pa). Mastering a few canonical conversion constants prevents costly mistakes in structural, hydraulic, and machine design computations.


Given Data / Assumptions:

  • Standard gravity g0 = 9.80665 m/s^2.
  • Force relation: 1 kgf = 9.80665 N; therefore 1 N ≈ 0.10197 kgf.
  • Pressure: 1 kgf/cm^2 = 9.80665 * 10^4 N/m^2 = 98.0665 kN/m^2.
  • Standard atmosphere: 1 atm = 101.325 kPa = 101.325 kN/m^2.


Concept / Approach:

Apply g0 to convert kgf ↔ N and scale area conversions carefully to move between cm^2 and m^2. Recognize 1 kPa = 1 kN/m^2 for pressure magnitudes in engineering usage.


Step-by-Step Solution:

From definition: 1 kgf = g0 N = 9.80665 N → invert to get 1 N ≈ 0.10197 kgf.For pressure: 1 cm^2 = 10^-4 m^2 → 1 kgf/cm^2 = 9.80665 N / 10^-4 m^2 = 98,066.5 N/m^2 = 98.0665 kN/m^2.Atmospheric pressure: 1 atm = 101,325 N/m^2 = 101.325 kN/m^2.


Verification / Alternative check:

Compare with common engineering rules of thumb: 1 kgf/cm^2 ≈ 0.980665 bar and 1 atm ≈ 1.01325 bar, showing consistency with the S.I. pascal scale (1 bar = 100 kPa).


Why Other Options Are Wrong:

  • Each A–D is individually correct; the most complete choice is E (All the above).


Common Pitfalls:

  • Forgetting the area conversion when moving from cm^2 to m^2, leading to 10^4 errors.
  • Applying g0 to masses instead of forces when converting kgf to N.


Final Answer:

All the above.

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