Question

The vernier constant (V.C.) of a vernier caliper is 0.01 cm. If 10 divisions of the vernier scale is equivalent to 9 divisions of the main scale then the value of one of the smallest division of the main scale is:
A) 1 cm
B) 1 mm
C) 0.1 mm
D) 0.01 cm

Answer 1

Hint: The vernier constant (V.C.) of a vernier calipers is the ratio of the smallest division on the main scale to the number of divisions on the vernier scale. The vernier constant is the least count of the instrument.
Using this ratio, we will find out the value of the smallest division on the main scale.
Formula used:
$\text{Vernier Constant (V}\text{.C}\text{.) = }\dfrac{\text{value of the smallest division on the main scale}}{\text{Number of divisions on the vernier scale}}$

Complete step by step answer:
The vernier calipers is an instrument used to measure length. It has two scales, a main scale and the vernier scale. The main scale remains fixed, while the vernier scale slides over the main scale. Usually the last division of the vernier scale coincides with the second last division of the main scale. This is used to find out the vernier constant (V.C) or least count of the instrument.
The vernier constant (V.C.) of a vernier calipers is the ratio of the smallest division on the main scale to the number of divisions on the vernier scale. The vernier constant is the least count of the instrument. Therefore,
$\text{Vernier Constant (V}\text{.C}\text{.) = }\dfrac{\text{value of the smallest division on the main scale}}{\text{Number of divisions on the vernier scale}}$--(1)
Now, given the vernier constant (V.C) is 0.01 cm.
The number of the division on the vernier scale coinciding with the main scale (which is usually equal to the number of divisions on the vernier scale) is 10.
Putting this information in (1), we get,
$\text{Value of the smallest division on the main scale = Vernier constant}\times \text{No}\text{. of divisions on the vernier scale}$
$=0.01cm\times 10=0.1cm=1mm$ -----$\left( \because 0.1cm=1mm \right)$
Therefore, the value of the smallest division of the main scale is 1 mm.
Hence, the correct option is B) 1 mm.

Note: Most questions related to Vernier Calipers can be solved by writing the basic equations for finding out the Vernier Constant of the vernier calipers as given above and then plugging in the information given after analyzing it accordingly.
Often students make the mistake and get confused between the main scale and the vernier scale. They should remember that the main scale is the fixed scale that helps to take a gross reading while the vernier scale allows us to make a more accurate reading.
The equation for finding out the least count of a vernier scale must be very clear to the students.
Thus, the process for finding out the vernier constant should be clear to a student. This will not only help in questions, but also in the laboratory, when one has to use this device practically.