Linear and Angular Measurement Questions and Answers

Answer: D

Optical flats use the interference of light waves for measuring very small linear dimensions, such as flatness, with high accuracy. A flat is placed on the surface and monochromatic light produces interference fringes, whose pattern shows the deviation in fractions of a wavelength. A sine bar measures angles, a vernier caliper and a micrometer measure by mechanical scales and screw threads, so they do not use interference.

Each fringe stands for a height difference of half a wavelength, about 0.3 micrometre for visible light, so a flat reads out flatness to a fraction of a micrometre.

Answer: B

One degree equals 60 minutes.

Angles are divided sexagesimally: 1 degree = 60 minutes (60') and 1 minute = 60 seconds (60"), so 1 degree = 3,600 seconds.

60 seconds is one minute of arc, not one degree. The options with 100 seconds and 100 minutes come from a decimal system; the centesimal grade (gon) divides a right angle into 100 parts, but it is not how a degree is subdivided.

Answer: C

The least count is 0.01 mm.

Least count is one main scale division minus one vernier scale division. Since 50 vernier divisions equal 49 main divisions of 0.5 mm:

\[ \begin{aligned} 1\ \text{VSD} &= \frac{49 \times 0.5}{50} = 0.49\ \text{mm} \\ \text{LC} &= 0.5 - 0.49 = 0.01\ \text{mm} \end{aligned} \]

Equivalently, LC = MSD / number of vernier divisions = 0.5/50 = 0.01 mm. 0.1 mm would need only 5 vernier divisions; 1 mm and 10 mm are larger than a main scale division and cannot be a vernier's least count.

Answer: B

The indirect angle measuring tool is the bevel gauge.

A bevel gauge has a blade that can be set to any angle and locked, but it carries no graduations. It copies an angle from the work and transfers it, and the angle is then read with a protractor. Measuring through a second instrument is what makes it indirect.

A bevel protractor reads angles directly off its vernier scale. The protractor head of a combination set also reads angles directly. A marking table is a flat reference surface for marking out and does not measure angles.

Answer: A

The thickness of piping is measured with a tube micrometer.

A tube micrometer has a rounded or cylindrical anvil, often set at right angles to the frame, that fits inside the bore of the tube and contacts its curved inner surface at a single point. The spindle closes on the outer surface, so the reading gives the wall thickness directly.

A depth micrometer measures the depth of holes, slots and steps. A flange micrometer has thin discs for measuring the thickness of flanges and narrow lands. Micrometer stops are accessories that set a fixed length, not a separate type of measuring micrometer.

Answer: C

The diameter of the rod is 114.68 mm.

A 100-125 mm micrometer reads from 100 mm, so its scale reading must be added to 100. A metric micrometer with 0.5 mm pitch and 50 thimble divisions has a least count of 0.01 mm:

\[ \begin{aligned} \text{reading} &= 100 + 14.5 + 18 \times 0.01 \\ &= 100 + 14.5 + 0.18 = 114.68\ \text{mm} \end{aligned} \]

14.68 mm forgets the 100 mm starting size of the instrument, and 14.70 mm forgets it too. 114.18 mm drops the 0.5 mm half-division showing on the barrel.

Answer: C

The minimum is 8 mm.

Telescopic gauges come in sets whose smallest gauge covers holes from about 8 mm to 12.7 mm, with the largest reaching about 150 mm. The spring-loaded plungers are locked at the bore size and the gauge is then measured with an outside micrometer.

12.7 mm is the upper limit of the smallest gauge, not the minimum, and 150 mm is the top of the set's range. For holes smaller than about 8 mm, small hole gauges are used instead. (The paper prints this option with the letter B as well; options are given here in printed order.)

Answer: B

The locknut is provided to lock the reading after setting it over the workpiece.

Once the spindle has been closed on the work, the locknut (spindle lock) is tightened so that the spindle cannot turn. The micrometer can then be withdrawn and read without the setting changing, and it can be used as a fixed gauge for checking several parts.

The thimble and ratchet, not the locknut, control the movement of the spindle and give a consistent measuring pressure. Accuracy comes from the screw and the scales. Locking the spindle when the instrument is put away is not its purpose; micrometers are in fact stored with the faces apart and unlocked.

Answer: A

Flatness and squareness are checked with a try square.

The blade of a try square is a precise straight edge at 90 degrees to its stock. Laid on a surface it shows flatness by the light gap under the blade, and with the stock against one face it shows whether an adjacent face is square to it.

A bevel gauge transfers or sets angles other than 90 degrees. Slip gauges are precision length standards. A vernier height gauge measures and marks heights from a surface plate; none of them is the everyday tool for both checks.

Answer: B

The least count of a vernier bevel protractor is 5’ (five minutes).

The main scale is graduated in degrees, and the vernier has 12 divisions on each side of its zero, spanning 23 degrees. One vernier division is therefore 23/12 degrees, or 1 degree 55 minutes, which falls short of two main-scale degrees by 5 minutes of arc.

1’ and 0.5’ would need a far finer vernier than a bevel protractor carries, and 10’ is twice the actual least count.