Question

A screw gauge of pitch \[1mm\] has a circular scale divided into 100 divisions. The diameter of a wire is measured by the above said screw gauge. The main scale reading is 1mm and 47th circular division coincides with the main scale. Find the curved surface area of wire in true significant figures. (Given the length of wire is equal to \[5.6cm\] and there is no zero-error in the screw gauge)

Answer 1

Hint: Usually, screw gauge measurement is based on two parameters and they are pitch and least count. The minimum length that can be measured by a screw gauge is called its Least Count. It is mostly used for measuring the diameter of circular objects. And the pitch defines the distance moved by the spindle per revolution.

Complete step by step answer:
Least Count = \[\dfrac{{1mm}}{{100}} = 0.01mm\]
As we know that,
Diameter= M.S + No of divisions coinciding with main scale x least count
\[ 1mm + 47 \times 0.01mm\]
\[\Rightarrow 1.47mm = 0.147cm\]
Now,
Curved Surface Area = \[\pi dl\]
$\Rightarrow$ Curved Surface Area = \[ \dfrac{{22}}{7} \times 0.147 \times 5.6\]
$\therefore$ Curved Surface Area = \[ 2.6c{m^2}\]

Therefore, the curved surface area of wire will be \[2.6c{m^2}\].

Additional Information:
Some steps of screw gauge measurement using micrometer:
The Structure of the Screw Gauge: Some sections are stationary such as Sleeve, Spindle, Anvil, Frame, and Thimble while some sections are movable.
Clean the anvil and spindle before the measurement: We should take a clean cloth or a paper and place it between the spindle and anvil. Then, you should firm the setup slightly till the cloth/paper settles and then pull it out. This step helps us to get an accurate result of measurement.
Object should be placed between the spindle and anvil: Carefully, fix the object in between the anvil and the spindle. As we know that anvil is stationary in nature, thus it is always good to place the object against it. The object should not move while recording the measurements, thus place it with extra care.

Note:Screw gauge can be supposed the best instrument for precise measurement of spherical as well as cylindrical objects. Usually, the pitch of a screw gauge is 1mm. The pitch of the screw gauge can be expressed as distance moved by the screw/number of rotations.