Question

Thickness of a pencil measured by using a screw gauge (least count 0.001cm) comes out to be 0.802 cm. The percentage error in the measurement is
A) 0.125%
B) 2.43%
C) 4.12%
D) 2.14%

Answer 1

Hint: To solve this problem one must know what actually a least count is and how it can be used to find out the error in measurement. Let us first what is the least count. The least count of a measuring instrument is the smallest measurement that can be taken with the instrument itself.

Complete step by step solution:
It is given in the problem that the least count (L.C.) of the screw gauge is 0.001 cm. I.e. $L.C. = 0.001cm$
Also, the measured value (M.V.) of the thickness of the pencil is given to be 0.802 cm. I.e. $M.V. = 0.802cm$
Now we know that the error in measurement is taken to be its least count. Therefore total error (T.E.) is given by, $T.E. = \left( {0.802 \pm 0.001} \right)cm$
Whereas the absolute error (A.E) is the least count of the screw gauge, i.e $A.E. = 0.001cm$
The percentage error is calculated by taking the ratio of absolute error to the measured value and then multiplying this ratio by 100. Hence, mathematically we have the following expression.
$\% Error = \dfrac{{A.E}}{{M.V.}} \times 100\% $ ………….. (1)
Putting the values of A.E and M.V. in equation (1) we get,
$\% Error = \dfrac{{0.001}}{{0.802}} \times 100\% $
$ \Rightarrow \% Error = 0.1247\% $
The value of percentage error in the measurement of the thickness of the pencil comes out to be 0.1247% which is almost equal to 0.125%.

Hence, we can say that option A is the correct answer.

Note: A screw gauge is an instrument used for accurate measurement of geometrical parameters like width, breadth, thickness, diameter etc. of any component. The screw gauge is also referred to as a micrometer screw gauge. A screw gauge is widely used in machining and mechanical engineering.