In a Vernier calliper, 39 main scale divisions are divided into 40 equal points on the Vernier scale. Then what is its least count (LC) in mm? (Take the value of main scale division = 1mm).
0.025
This question asks for the calculation of the least count (LC) of a Vernier caliper based on specific information about its main scale divisions (MSD) and Vernier scale divisions (VSD).
Vernier Caliper Basics
A Vernier caliper is a precision measuring instrument used to measure linear dimensions accurately. It consists of two scales:
- Main Scale: Similar to a ruler, marked in millimeters (mm) or centimeters (cm).
- Vernier Scale: A sliding scale that moves along the main scale, allowing for more precise readings than the main scale alone.
The precision of a Vernier caliper is determined by its least count, which is the smallest measurement that can be accurately measured using the instrument.
Least Count Calculation
The least count (LC) of a Vernier caliper can be calculated using the following relationship:
Formula 1: LC = 1 MSD - 1 VSD
Where:
1 MSDis the value of one Main Scale Division.1 VSDis the value of one Vernier Scale Division.
Alternatively, a more direct formula can be used when the specific condition mentioned in the problem is met:
Formula 2: LC = Value of 1 MSD / Total Number of Divisions on Vernier Scale
Applying the Formulas to the Problem
From the question, we are given:
- Value of 1 Main Scale Division (
1 MSD) = 1 mm - Number of Main Scale Divisions covered by Vernier Scale = 39
- Total Number of Divisions on the Vernier Scale = 40
This means that 40 Vernier Scale Divisions (40 VSD) are equal to 39 Main Scale Divisions (39 MSD).
Step-by-Step Calculation using Formula 2:
- Identify the value of 1 MSD:
1 MSD = 1 mm - Identify the total number of divisions on the Vernier Scale:
Total VSD = 40 - Apply the formula:
LC = Value of 1 MSD / Total Number of Divisions on Vernier Scale - Substitute the values:
LC = 1 mm / 40 - Calculate the result:
LC = 0.025 mm
Verification using Formula 1:
- We know
40 VSD = 39 MSD. - Calculate the value of 1 VSD:
1 VSD = (39 / 40) * 1 MSD - Substitute the value of 1 MSD:
1 VSD = (39 / 40) * 1 mm = 0.975 mm - Calculate the Least Count:
LC = 1 MSD - 1 VSD - Substitute the values:
LC = 1 mm - 0.975 mm - Calculate the result:
LC = 0.025 mm
Both methods yield the same result.
Conclusion
The least count of the Vernier caliper described in the question is 0.025 mm.
Important Questions from Caliper
How many divisions are graduated on the thimble of micrometer?
The least count of Vernier bevel protractor is ____
Why are calipers generally used along with a steel rule in workshop measurement?
In a vernier caliper, the small scale that slides along the main scale is called:
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?
