Question

One centimeter on a scale is divided into 20 equal divisions. The least count (minimum value) of this scale is
A.\[20\,{\text{cm}}\]
B.\[1\,{\text{mm}}\]
C.\[0.1\,{\text{mm}}\]
D.\[0.5\,{\text{mm}}\]

Answer 1

Hint: Use the formula for the least count of an instrument. This formula gives the relation between the main scale reading of the instrument and the total number of divisions on the secondary scale.

Formula used:
The formula for the least count of an instrument is given by
\[{\text{Least count}} = \dfrac{{{\text{Main scale reading}}}}{{{\text{Total number of divisions on main scale}}}}\] …… (1)

Complete step by step answer:
On the scale, one centimeter is divided into 20 equal divisions.

Hence, the main scale reading for the scale is \[1\,{\text{cm}}\] and the total number of divisions on the secondary scale is 20.

Calculate the least count of the given scale.

Substitute \[1\,{\text{cm}}\] for \[{\text{Main scale reading}}\] and 20 for \[{\text{Total number of divisions on main scale}}\] in equation (1).
\[{\text{Least count}} = \dfrac{{1\,{\text{cm}}}}{{{\text{20}}}}\]
\[ \Rightarrow {\text{Least count}} = 0.05\,{\text{cm}}\]

Hence, the least count of the given scale is \[0.05\,{\text{cm}}\].

Convert the unit of the least count of the given scale from centimeter to millimeter.
\[{\text{Least count}} = \left( {0.05\,{\text{cm}}} \right)\left( {\dfrac{{10\,{\text{mm}}}}{{1{\text{cm}}}}} \right)\]
\[ \Rightarrow {\text{Least count}} = 0.5\,{\text{mm}}\]

Therefore, the least count of the given scale is \[0.5\,{\text{mm}}\].

So, the correct answer is “Option D”.

Additional Information:
The least count of an instrument is defined as the least or minimum value which the instrument can measure with precision.
The value of the least count gives the information that which instrument should be used to measure a particular length or directly measurable physical quantity.
The least count is the ratio of main scale reading to the number of divisions on main or secondary scale.
For example, the main scale reading of the vernier caliper is 1 cm and the total number of divisions on the main scale is 10. Hence, the least count for the main scale of the vernier caliper is 0.1 cm.

Note:
Since the scale has only the main scale, the total number of divisions on the main scale is considered. But some instruments have a secondary scale also. For such instruments, the number of divisions on the secondary scale is used in the formula.