Scales Questions and Answers

Answer: C

Ten vernier divisions occupying nine main divisions means each differs by a tenth of a main division, and the coincident line gives the reading. The same principle serves on a calliper, a theodolite and a drawing scale.

Answer: D

Correct answer: difference between one main and one vernier division

The least count is the amount by which one main scale division exceeds one vernier division, and it is the smallest quantity the instrument can resolve. Making the vernier divisions slightly shorter than the main ones means that only one pair of lines coincides at a time, and which pair it is gives the fraction directly.

Answer: A

Correct answer: greater precision than the diagonal construction gives

A vernier resolves finer than a diagonal scale of comparable size, because the resolution depends on the difference between two nearly equal divisions rather than on how finely a line can be subdivided by eye. The price is that it must be made and read with greater care, and a misread coincidence gives a wrong answer with no warning.

Answer: B

Correct answer: read the same length in two different systems of units

Comparative scales are two scales drawn to the same representative fraction on a common base line, one graduated in each system, so a length set off on one can be read directly on the other. They are used where a drawing must serve users working in different units, and no arithmetic is needed to convert.

Answer: C

Correct answer: the same representative fraction

This is what makes the comparison possible: both scales reduce the world by the same factor, so a given physical distance occupies the same length on the paper in both, and can be read off either. Their divisions and total lengths will differ, since the units differ, but the reduction must be identical.

Answer: D

Correct answer: set out and measure angles without a protractor

A scale of chords gives the chord length subtending each angle at a circle of a chosen radius, so an angle is constructed by striking an arc of that radius and stepping off the chord taken from the scale. It is the classical means of setting out angles with dividers alone, and it is exact rather than approximate.

Answer: A

Correct answer: the radius of the arc used

The chord of 60 degrees equals the radius, because the chord, the radius to each end and the arc form an equilateral triangle. This is the property the scale is built on: the 60 degree mark is set at the radius, which fixes the scale, and every other chord is stepped off from the same arc.

Answer: B

Correct answer: the drawing sheet or survey chain has altered in length

A shrunk scale corrects for a physical change in the measuring medium. Paper contracts with age and changes in humidity, and a survey chain stretches with use, so lengths taken from the one or recorded with the other are no longer what they purport to be. The shrunk scale builds the correction into the graduations.

Answer: C

Correct answer: shrunk length to the original length

The shrinkage factor is the ratio of what a line now measures to what it measured when drawn, so a 20 cm line reading 19.5 cm gives 0.975. Being less than one for a contraction, it can be multiplied directly into the representative fraction, which is what makes it the convenient form of the correction.

Answer: D

Correct answer: shrinkage factor

The paper has contracted, so a given drawing length now represents a greater actual length than it did, and the representative fraction must be reduced accordingly. Multiplying by the factor does exactly that: a nominal 1/1000 with a factor of 0.975 becomes 0.975/1000, or about 1/1026 - a smaller fraction, not a larger one.