To find the diameter of the cylinder using a vernier caliper, we need to follow a systematic approach to interpret the measurements accurately. Let's break this down step by step.
Understanding the Measurement Components
In your scenario, the vernier caliper has a main scale and a vernier scale. The main scale is marked in centimeters, while the vernier scale allows for more precise measurements. Here’s how we can calculate the diameter:
Step 1: Identify the Main Scale Reading
The zero of the vernier scale lies between 5.10 cm and 5.15 cm on the main scale. This means the main scale reading (MSR) is:
Step 2: Determine the Vernier Scale Reading
The vernier scale has 50 divisions that equal 2.45 cm. To find the value of one division on the vernier scale (VSD), we can use the formula:
- VSD = Total length of vernier scale / Number of divisions
- VSD = 2.45 cm / 50 = 0.049 cm
Next, we need to find which division on the vernier scale aligns with a division on the main scale. You mentioned that the 24th division of the vernier scale coincides with a division on the main scale. Therefore, the vernier scale reading (VSR) is:
- VSR = 24 × VSD = 24 × 0.049 cm = 1.176 cm
Step 3: Calculate the Total Diameter
Now, we can find the total reading, which gives us the diameter of the cylinder:
- Diameter = MSR + VSR
- Diameter = 5.10 cm + 1.176 cm = 6.276 cm
Final Result
Thus, the diameter of the cylinder is approximately 6.276 cm.
This method of using a vernier caliper allows for precise measurements, which is crucial in various scientific and engineering applications. If you have any further questions or need clarification on any part of this process, feel free to ask!
