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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?
Most Upvoted Answer
The diameter of a cylinder is measured using a vernier callipers with ...
Given Data:
- Zero error: between 5.10 cm and 5.15 cm
- Vernier scale: 50 divisions equivalent to 2.45 cm
- 24th division of vernier scale coincides with a main scale division

Solution:

Step 1: Calculate the main scale reading
- The zero error lies between 5.10 cm and 5.15 cm
- Therefore, the main scale reading = Zero error + Reading on main scale
- Reading on main scale = 5.10 cm

Step 2: Calculate the vernier scale division
- Total length of the main scale division = 0.05 cm (5.10 cm - 5.15 cm)
- Total length of the vernier scale = 2.45 cm
- Length of 1 vernier scale division = Total length / Total divisions
- Length of 1 vernier scale division = 2.45 cm / 50 = 0.049 cm

Step 3: Find the actual reading by aligning the main and vernier scales
- To find the actual reading, find which vernier scale division coincides with the main scale
- Given that the 24th division of the vernier scale coincides with a main scale division
- Actual reading = Main scale reading + (Vernier scale division x Value of 1 division on main scale)
- Actual reading = 5.10 cm + (24 x 0.049 cm)
- Actual reading = 5.10 cm + 1.176 cm
- Actual reading = 5.276 cm
Therefore, the diameter of the cylinder is 5.276 cm. However, since the zero error is in the range of 5.10 cm to 5.15 cm, we need to subtract the zero error to get the correct reading.

Corrected Diameter:
- Corrected diameter = Actual reading - Zero error
- Corrected diameter = 5.276 cm - 5.10 cm
- Corrected diameter = 0.176 cm
- Corrected diameter = 5.124 cm
Therefore, the correct diameter of the cylinder is 5.124 cm, which corresponds to option B.
Free Test
Community Answer
The diameter of a cylinder is measured using a vernier callipers with ...
1 MSD = 0.05 ​

Diameter of the cylinder
= MSR + L.C. × 24
= 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 isa)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 isa)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 isa)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 isa)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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