Question

When a screw gauge with a least count of 0.01 mm is used to measure the diameter of a wire, the reading on the sleeve is found to be 1 mm and the reading on the thimble is found to be 27 divisions.
A. What is the diameter of the wire in cm?
B. If the zero error is +0.005 cm, what is the correct diameter?

Answer 1

Hint: Several times we need to be very precise about our measurements. The most commonly used equipment or device for measurement is scale. It can be used to measure the length in order of milli-meter. It can’t measure the distance of order one-tenth of milli-meter. Hence the minimum it can measure is called its least-count. But what if we need to calculate even more precisely? In that case we go for even accurate devices such as screw-gauge and Vernier caliper.

Complete step by step answer:
The least count of different devices is different. The minimum the value of the least count of a device, the accurate is it’s measurement. The least count of screw-gauge is 0.01 means it is 100 times more accurate than a meter scale.
Now, in order to calculate the diameter of the wire, we are given:
$L.C = 0.01 mm$
Measured value = 1mm
No. of divisions = 27
Thus using Reading = measured value + (number of division) x (Least count)
Hence:
$Reading = 1mm + 0.01 \times 27 = 1 + 0.27 = 1.27 mm$
Hence the diameter of wire is 1.27mm = 0.127 cm
Now, zero if zero error is +0.005cm means when the mark is at zero, the actual reading is 0.005cm at that time.
Hence the measured value is greater by 0.005cm
Thus to get correct value, we must subtract 0.005cm from the calculated value:
Thus actual value = $0.127cm - 0.005 cm = 0.122 cm$

Note:
Screw gauge contains a screw which is used to adjust the width of the opening of the screw-gauge. First it is sufficiently opened such that the specimen can be fit perfectly inside the gauge and then the screw is turned slowly till it gets tightened up. After if stops rotate, no. of divisions are noted and length is calculated.