Solved Examples on Vernier Callipers
Example 1: A Vernier Calliper with no zero error is used to measure the diameter of a cylinder. The zero of the Vernier scale is observed between 4.20 cm and 4.25 cm on the main scale. The Vernier scale consists of 50 divisions, which are equivalent to 2.45 cm. The 11th division on the Vernier scale coincides exactly with one of the divisions on the main scale. What is the diameter of the cylinder?
Solution:
To find the diameter, we consider the following information:
- Smallest division on the main scale = 0.05 cm (4.25 – 4.20)
- Main scale reading = 4.20 cm,
- Vernier coincidence = 24
- Least Count = 0.05 – 2.45/50 = 0.001 cm.
Using these values,
Diameter = Main Scale Reading + (Vernier Coincidence × Least Count)
Diameter = 4.20 + 11 × 0.001
Diameter = 4.211 cm
Thus, the diameter of the cylinder is 4.211 cm
Example 2: A Vernier Calliper is used to measure the diameter of a cylinder. The main scale of the Calliper is calibrated in millimeters, and it is observed that 15 divisions on the main scale are equal in length to 20 divisions on the Vernier scale. When measuring the diameter, the main scale reading is 45 divisions, and the 8th division on the Vernier scale coincides with a division on the main scale. Find the least count of the vernier Calliper and the radius of the cylinder.
Solution:
(i) To Determine the Least Count:
MSD (Main Scale Division) = 0.1 cm
20 VSD (Vernier Scale Division) = 15 MSD
Therefore,
VSD = (19/20) MSD = (15/20) × 0.1 cm = 0.075 cm
Least Count = MSD – VSD
Least Count = 0.1 cm – 0.075 cm
Least Count = 0.025 cm
Thus, the least count of the vernier Calliper is 0.025 cm.
(ii) To Find the Radius:
Main Scale Reading = 45 mm = 4.5 cm
Diameter = Main scale reading + (vernier coincidence × least count)
Diameter = 4.5 cm + (8 × 0.025 cm)
Diameter = 4.5 cm + 0.2 cm
Diameter = 4.7 cm
Radius = Diameter/2 = 4.7/2 = 2.35 cm
Thus, the radius of cylinder is 2.35 cm
Also Check:
Vernier Calliper
Vernier Calliper is a precision measuring instrument used to measure the internal and external dimensions of an object. It consists of two main parts:
- A Fixed Jaw
- A Movable Jaw
The fixed jaw is used to measure the outside of an object, while the movable jaw is used to measure the inside of an object. This is a device that is used to measure very smaller values and it can measure the value in the range of 0.1 mm.
In this article, we will learn about Vernier Calliper, its diagram, working, and others in detail.