Question

A student measured the diameter of a small steel ball using a screw gauge of least count $0.001 \mathrm{cm} .$ The main scale reading is $5 \mathrm{mm}$ and zero of circular scale division coincides with $25 divisions$ above the reference level. If the screw gauge has a zero error of $-0.004 \mathrm{cm},$ the correct diameter of the ball is?
(A) $0.053 \mathrm{cm}$
(B) $0.521\text{cm}$
(C) $0.529\text{cm}$
(D) $0.525\text{cm}$

Answer 1

Hint
The screw gauge is defined to be an instrument that is used for measuring exactly the diameter of a thin wire or the width of a sheet of a metal. It comprises a U-shaped mount which is fixed with a screwed pin which is fixed to a thimble. The least count of a screw gauge is $0.01mm$. Based on this concept we have to find the answer to this question.

Complete step by step answer
The Least count of the screw gauge is $=0.001 \mathrm{cm}$
The main scale reading of the screw gauge is $\mathrm{R}=5 \mathrm{mm}$ and $25 divisions$ above the reference level.
Zero error in the screw gauge $=-0.004 \mathrm{cm}$
Observed reading of the screw gauge$=0.5+25 \times 0.001$
$=0.5+0.025$
$=0.525\text{cm}$
Actual reading $=0.525+0.004$
$=0.529 \mathrm{cm}$
Therefore, the correct answer is Option (C).

Note
We should know the smallest value that can be measured by the measuring instrument is known as the least count of that instrument. We should also know that the least count error is defined as the error that is associated with the revolution of the instrument.