Q.7 Which of the following scales may NOT give accurate measurements of a plan drawn on a paper, due to shrinkage after few years?
- AEngineer's scale and representative fractionCorrect
- BRepresentative fraction and graphical scale
- CEngineer's scale and graphical scale
- DGraphical scale
Solution
Concept
A graphical scale is drawn on the same paper, so it shrinks with the plan. Numerical scales (engineer's scale, RF) do not shrink.
Formula
Shrinkage factor = shrunk length / original length; Corrected scale = original scale × shrinkage factor
Step-by-step solution
1. After some years, the paper and the plan on it shrink. 2. The engineer's scale (e.g. 1 cm = 10 m) and the RF (e.g. 1/1000) are written as numbers. Numbers do not shrink. 3. So distances measured with these numerical scales on the shrunk plan will be wrong. 4. A graphical scale is a line drawn on the same paper. It shrinks in the same ratio as the plan. 5. So the graphical scale still gives correct results. 6. Scales that may NOT be accurate = engineer's scale and RF. Answer (A).
Explanation
When paper shrinks, every line on it becomes shorter, including the graphical scale line. The graphical scale changes in the same ratio as the plan, so it stays correct. The engineer's scale and RF are fixed numbers and cannot change with the paper, so they give wrong measurements.
Why the other options are wrong
B: Graphical scale is accurate, so it should not be included. C: Graphical scale is accurate, so it should not be included. D: Graphical scale is the only scale that remains accurate.
Shortcut
Graphical scale shrinks with the paper, so it is always correct. Pick the option without 'graphical scale'.
Common mistake
Thinking a graphical scale is affected by shrinkage. It is, but in the same ratio as the plan, so the error cancels.
Correct answer: A) Engineer's scale and representative fraction