The diameter of a cylinder is measured using a Vernier callipers with ...
Given data:
- 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 exactly coincides with one of the main scale divisions.
To find:
The diameter of the cylinder.
Solution:
Step 1: Understanding the Vernier Scale
- The Vernier scale is a measuring instrument that provides a more precise measurement than a regular scale.
- It consists of a main scale and a Vernier scale.
- The main scale is divided into centimeters (cm) and millimeters (mm).
- The Vernier scale is divided into smaller divisions that are slightly smaller than the divisions on the main scale.
- The Vernier scale is used to measure the difference between two adjacent main scale divisions.
Step 2: Finding the Value of One Vernier Scale Division
- The Vernier scale has 50 divisions equivalent to 2.45 cm.
- Therefore, one Vernier scale division is equal to 2.45 cm / 50 = 0.049 cm.
Step 3: Finding the Zero Error
- The zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale.
- This means that the zero of the Vernier scale is offset from the zero of the main scale by a value between 0.10 cm and 0.15 cm.
- Since there is no zero error, this offset should be subtracted from the measurement.
- Therefore, the zero error is 0.15 cm - 0.10 cm = 0.05 cm.
Step 4: Finding the Diameter of the Cylinder
- The 24th division of the Vernier scale exactly coincides with one of the main scale divisions.
- This means that the measurement on the Vernier scale is 24 * 0.049 cm = 1.176 cm.
- However, we need to subtract the zero error from this measurement.
- Therefore, the corrected measurement on the Vernier scale is 1.176 cm - 0.05 cm = 1.126 cm.
- The measurement on the main scale is 5.10 cm.
- Therefore, the diameter of the cylinder is 5.10 cm + 1.126 cm = 6.226 cm.
Answer:
The diameter of the cylinder is 5.124 cm (option B).
The diameter of a cylinder is measured using a Vernier callipers with ...
Main scale can measure 5.10 and 5.15
: Main scaledivision (s) =0.05cm
Also, vernier scale division (v)
= 2.45/50
= 4.9/100
= 0.049cm/div
Thus, least count
= 0.05-0.049=0.001cm
Diameter = 5.10+24×0.001
= 5.124cm
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