Question

The Vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5mm, then the least count of the microscope is
A. 0.02mm
B. 0.05mm
C. 0.01mm
D. 0.1mm

Answer 1

Hint: Least count of travelling microscopes can find out from the difference between the one main scale division and one Vernier scale division. The ratio of one main scale division to the total number of Vernier scale divisions is also possible to find out the least count of the travelling microscope.

Formula used:
$\text{Least count = }\dfrac{\text{Smallest division on the main scale}}{\text{Total number of divisions on the Vernier scale}}$

Complete step-by-step answer:
Least count is the smallest value that can be measured by an instrument. It is the ratio of smallest division on the main scale to the number of divisions on the Vernier scale.
$\text{Least count = }\dfrac{\text{Smallest division on the main scale}}{\text{Total number of divisions on the Vernier scale}}$
Here the smallest division is 0.5 mm and the number of divisions in the Vernier scale is 50. Thus, the least count will be,
$\text{Least count = }\dfrac{0.5mm}{50}$
$\text{Least count = 0}\text{.01mm}$
We can do this in another method also.
In the question, we have seen that 50 Vernier scale divisions coincide with the 49 main scale divisions. So we can write this as,
$\text{50 V}\text{.S}\text{.D = 49}\times \text{one main scale division}$
$\text{50 V}\text{.S}\text{.D = 49}\times 0.5mm$
$\text{V}\text{.S}\text{.D = }\dfrac{\text{49}}{50}\times 0.5mm$
So, one Vernier scale division will be,
$\text{V}\text{.S}\text{.D = 0}\text{.49mm}$
The least count can be written as the difference between one main scale division and one Vernier scale division.
$\text{Least count = }\left[ 0.5-\left( \dfrac{49}{50} \right)\times 0.5 \right]$
$\text{Least count = }\left[ 0.5-0.49 \right]$
$\text{Least count = 0}\text{.01mm}$
Therefore the correct option is C.

Additional information:
To find the length with a Vernier scale instrument, we have to use this formula.
$\text{Length = MSR+(VSR}\times \text{ LC)}$, where MSR is the main scale reading, VSR is the Vernier scale reading and LC is the least count of the equipment.
While reading the measurements, we have to find if there is any error or not. There are two types of error that will occur in the Vernier scales. Positive and negative zero errors. Positive zero error is the additional readings right to the zero even when the two joints are in contact. So, we have to subtract this from the obtained measurement. Negative zero error is the additional readings left to the zero even when the two joints are in contact. So, we have to add these values to the measured values. If the system is too accurate, then zero error will not be there.

Note: Least count of equipment is very important when we are going from large scale readings to small scale readings. Incorrect readings will make wrong values. To make the system as accurate we are dealing with two scales. One is the main scale and the other one is the Vernier scale. The combined result will give accurate values.