Question

What is the least count of a meter scale?
A. \[1m\]
B. \[1cm\]
C. \[1mm\]
D. None of these

Answer 1

Hint: Smallest measurement that can be taken with the instrument is known as least count.
The following equation can be used for the calculation of least count.\[\text{Least count = }\dfrac{\text{Magnitude of one division}}{\text{Number of divisions}}\]

Complete step by step answer:
Least count can help us to find the smallest unit that can measure with the particular instrument. It is directly depending upon the error of that instrument. If the least count is very small the accuracy of that instrument will be higher.
In a \[1cm\] of magnitude, a metre scale has \[10\] divisions of millimetres.
According to the expression of the least count,
\[\text{Least count = }\dfrac{\text{Magnitude of one division}}{\text{Number of divisions}}\]
\[\text{Least count = }\dfrac{1}{10}=0.1cm\] or \[1mm\]
Hence the correct option is C.

Additional information:
For Vernier instruments, least count will be the ratio of value of minimum deviation on the main scale to the number of divisions on the auxiliary scale.
Least count of screw gauge can be written as,
\[\text{Least count = }\dfrac{0.5}{50}\]
\[\text{Least count}=0.01mm\]
Screw gauge is commonly used to find the thickness of wire and thick films in laboratories. It is worked with the principle of screw and nut. A screw which can rotate attached to the concentric cylinder. One revolution by the screw rotation will bring the main scale and auxiliary scale in the same line. i.e. Its axial movement will be equal to the pitch of the screw.
Errors in Vernier calliper can be generated
Due to the wear and wrapping of jaws
Due to the excessive force on the moving jaw
Due to the non-alignment of auxiliary scale and main scale
Least count of Vernier callipers can be written as,
\[\text{Least count = }\dfrac{1}{10}\]
\[\text{Least count}=0.1mm\]

Note: Candidates are advised to use the units of least count perfectly. Otherwise the answer will be wrong. The least count will be the same unit of the magnitude of one division. So correspondingly we can alter the unit of least count into the required unit.
Least count of metre scale can be written as, \[0.1cm\] or \[1mm\] according to our requirement.