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The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that 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. The diameter of the cylinder is:
  • a)
    5.112 cm
  • b)
     5.124 cm
  • c)
    5.136 cm
  • d)
    5.148 cm
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The diameter of a cylinder is measured using a Vernier callipers with ...
Smallest main scale division = 0.05 cm (5.15 – 5.10)
Main scale reading = 5.10 cm (comes just before the zero of the Vernier scale)
Vernier coincidence = 24
Least count =0.05 – 2.45/50 = 0.001 cm
Diameter
= Main Scale Reading + Vernier coincidence × Least Count
= 5.10 + 24 × 0.001 = 5.124 cm
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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.
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The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that 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. The diameter of the cylinder is:a)5.112 cmb)5.124 cmc)5.136 cmd)5.148 cmCorrect answer is option 'B'. Can you explain this answer?
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The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that 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. The diameter of the cylinder is:a)5.112 cmb)5.124 cmc)5.136 cmd)5.148 cmCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that 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. The diameter of the cylinder is:a)5.112 cmb)5.124 cmc)5.136 cmd)5.148 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that 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. The diameter of the cylinder is:a)5.112 cmb)5.124 cmc)5.136 cmd)5.148 cmCorrect answer is option 'B'. Can you explain this answer?.
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