Question

The least count of a screw gauge is $0.001cm$.The diameter of wire measured by it is $0.225cm$.Find out the percentage error in this measurement.
A. $0.05$
B. $0.001$
C. $0.44$
D. $0.11$

Answer 1

Hint: While we are measuring with an instrument, there are chances to get an error. We calculate the percentage error to know how close we are with the actual real value. Least count is the minimum value we can measure using any instrument. It is unique for every instrument.
Formula used:
$Error\% = \dfrac{{L.C}}{d} \times 100$
Where,
L.C= least count. Here the least count of screw gauge is $0.001cm$,
d= diameter of the wire
As we don’t know the actual value. We take least count as an error which is the minimum error that can occur.

Complete answer:.
The least count of a screw gauge= $0.001cm$
The diameter of wire measured by the screw gauge= \[0.225cm\]
Now we apply these values in the formula,
$Error\% = \dfrac{{L.C}}{d} \times 100$
\[Error\% = \dfrac{{0.001}}{{0.225}} \times 100\]
\[Error\% = 0.0044 \times 100\]

\[\therefore Error\% = 0.44\% \]

Hence the correct option is option C.

Additional information:
(i)The least count is the minimum measurement we can measure using the particular instrument. For example, we use the \[15cm\].In that scale the minimum value we can measure is \[1mm\]. Hence the least count of that scale is \[1mm\].
(ii)The least count is related to the precision and accuracy of the instrument. So it is directly proportional to the error of the instrument.
(iii)Finding the least count is very much helpful for instruments like screw gauge, Vernier calliper.
(iv)Vernier callipers, an instrument for making very accurate linear measurements which was first made by Pierre Vernier in 1631.In memorable of him, it was named as Vernier calliper.
(v)Vernier Callipers are used in science laboratories and in many quality control applications. Using the Vernier calliper, we can find the length of the rod like objects, the diameter of spheres, internal and external diameters of hollow cylinder-shaped objects and the depth of the small objects.
(vi)Using a screw gauge, we can find the length in micrometres. It has a head scale and pitch scale. Using these scales, we can find the accurate readings.
(vii)We can use the screw gauge for measuring the diameter of wire, capillary tube, etc. It is used in micrometres to measure the accurate diameter of the celestial bodies or microscopic objects.

Note:
When the true value and the measured value is given, we say the difference between these two values is the error. But here we don’t know the true value, so we assume the minimum value as an error.