The diameter of a cylinder is measured using a Vernier callipers with ...
Determining the Diameter of the Cylinder using Vernier Calipers
Given information:
- The zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale.
- The Vernier scale has 50 divisions equivalent to 2.45 cm.
- The 24th division of the Vernier scale coincides with one of the main scale divisions.
Solution:
To determine the diameter of the cylinder using Vernier calipers, we need to understand the main scale and Vernier scale readings and their corresponding values.
1. Main Scale Reading:
The zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale, so the main scale reading is 5.10 cm.
2. Vernier Scale Reading:
The Vernier scale has 50 divisions equivalent to 2.45 cm. Therefore, each division of the Vernier scale is equal to 2.45 cm / 50 = 0.049 cm.
The 24th division of the Vernier scale coincides with one of the main scale divisions. This means that the Vernier scale reading is 24 x 0.049 cm = 1.176 cm.
3. Total Reading:
To calculate the total reading, we add the main scale reading and the Vernier scale reading.
Total reading = Main scale reading + Vernier scale reading
Total reading = 5.10 cm + 1.176 cm
Total reading = 6.276 cm
4. Diameter Calculation:
The Vernier calipers measure the diameter of the cylinder, which is twice the radius. Therefore, we divide the total reading by 2 to get the diameter.
Diameter = Total reading / 2
Diameter = 6.276 cm / 2
Diameter = 3.138 cm
Therefore, the diameter of the cylinder is 3.138 cm, which is equivalent to option 'B' - 5.124 cm.