In a vernier caliper, 50 vernier scale divisions coincide with 49 main scale divisions. If one main scale division is 1 mm, what is the least count?
0.02 mm
To find the least count of a vernier caliper, we need to understand the concept of vernier scale and how it relates to the main scale.
The least count of a vernier caliper can be calculated using the formula:
\(\text{Least Count} = \text{Value of 1 Main Scale Division} - \text{Value of 1 Vernier Scale Division}\)
Let's calculate step by step:
Main Scale Division (MSD): It is given that 1 main scale division equals 1 mm.
Vernier Scale Division (VSD): 50 vernier scale divisions coincide with 49 main scale divisions. Therefore, one vernier scale division is:
\(1 \, \text{VSD} = \frac{49 \, \text{MSD}}{50} = \frac{49 \, \text{mm}}{50}\)
Now, calculate the least count:
\(\text{Least Count} = 1 \, \text{mm} - \frac{49}{50} \, \text{mm}\)
\(\text{Least Count} = \frac{50}{50} \, \text{mm} - \frac{49}{50} \, \text{mm}\)
\(\text{Least Count} = \frac{1}{50} \, \text{mm} = 0.02 \, \text{mm}\)
Thus, the least count of the vernier caliper is 0.02 mm.
This is why the correct answer is the option 0.02 mm.
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