Question

A student measured the diameter of a wire using a screw gauge with the least count 0.001cm and listed the measurements. The correct measurement is:
A. 5.3 cm.
B. 5.32cm.
C. 5.320 cm.
D. 5.3200 cm.

Answer 1

Hint: To solve this question, we should remember some basic points of the screw gauge. We will check the value that has a precision upto the least count of the instrument.

Complete Step-by-Step solution:
Micrometer screw gauge is a device used to determine the diameter of thin wires, the thickness of small sheets of glass, plastic, etc. This will scale up to 1/10 mm (or 0.01 mm = 0.001 cm) which is generally referred to as the least number of micrometers.
We know that the 100-division screw gauge pushes the size of the cap around the main axis by 1/100 mm-0.01 mm. That is the minimum value that the screw gauge can calculate and is considered to be the least counted. Or it is defined as the ratio of the pitch of the screw to the number of divisions on the circular scale.
The least count of the screw gauge can be calculated by the formula:
$
  {\text{least count of screw gauge}} = \dfrac{{{\text{pitch of screw gauge}}}}{{{\text{total number of divisions of circular scale}}}} = \dfrac{{1mm}}{{100}} \\
  {\text{least count of screw gauge}} = 0.01mm = \dfrac{{0.01}}{{100}}cm = 0.001cm \\
$
And now, we've got the least count of screw size, i.e. 0.001 cm.
Since the least count is 0.001 cm, the distance measured by the screw gauge should be in the multiple of 0.001.
Let's check for option (A)
$\therefore $ 5.3 cm – a multiple of 0.001 cm.
(b) option,
$\therefore $ 5.32 cm – this is not a multiple of 0.001 cm.
(c) option,
$\therefore $ 5.320 – a multiple of 0.001 cm
$ \Rightarrow \dfrac{{5.320}}{{0.001}} = 5320$
(d) option,
$\therefore $ 5.3200 – this is not a multiple of 0.001 cm.
We may therefore assume that the right measurement is 5.320 cm.
Therefore, choice (C) is the correct answer.

Note: Whenever we ask these types of questions, we first need to learn how to measure the lowest screw gauge count. Then we would realize the multiple of 0.001 must be the value that is determined by the screw gage. So, we 're going to test options that are 0.001 multiples. Through this we will get the answer.