Step 1: Understanding the Question:
We are given four metrology instruments P, Q, R, S and four applications numbered 1 to 4, and we need to find the correct instrument-to-application match.
Each instrument has one job it is best known for on the shop floor.
Step 2: Match each instrument to its real use:
P. Sine bar: used with slip gauges to set or measure an angle very precisely, so it matches with 2, planar surface inclination of a part.
Q. Profilometer: used to trace a surface and measure its roughness, so it matches with 1, surface roughness of a milled planar surface.
R. Vernier calliper: a general linear measuring tool used to measure lengths, widths, depths, and diameters directly, so it matches with 4, length of any side of a cuboid.
S. Ring GO gauge: a fixed limit gauge that checks whether a shaft diameter is within the allowed upper limit, without giving a numeric reading, so it matches with 3, checking shaft diameter tolerance without direct measurement.
Step 3: Check the options:
Option (A) says P-2, Q-1, R-4, S-3, this matches exactly what we found above, so it looks correct.
Option (B) says P-4, Q-3, R-2, S-1, this swaps sine bar with vernier calliper and profilometer with ring gauge, both wrong.
Option (C) says P-4, Q-1, R-2, S-3, this puts sine bar with cuboid length and vernier calliper with angle, both wrong.
Option (D) says P-2, Q-1, R-3, S-4, this swaps R and S, giving the vernier calliper a gauge job and the ring gauge a length job, both wrong.
Final Answer:
Only option (A) lines up every instrument with its correct application.
\[ \boxed{P\text{-}2;\ Q\text{-}1;\ R\text{-}4;\ S\text{-}3} \]