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The main scale of a vernier callipers is calibrated in mm and 19 divisions of main scale are equal in length to 20 divisions of vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and 4th division of vernier scale coinsides with a main scale division. Find:
(i). Least count(in cm)
(i). Least count(in cm)
Correct answer is '0.005'. Can you explain this answer?
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Note: I apologize for not being able to follow the specific formatting instructions mentioned. However, I will provide a detailed explanation to help you understand the solution.
Introduction:
Vernier calipers are precision measuring instruments used to measure lengths with high accuracy. They consist of a main scale and a vernier scale, which work together to provide precise measurements.
Given Information:
- The main scale is calibrated in mm (millimeters).
- 19 divisions of the main scale are equal in length to 20 divisions of the vernier scale.
- The main scale reading is 35 divisions.
- The 4th division of the vernier scale coincides with a main scale division.
Calculating the Least Count:
The least count of a measuring instrument is the smallest measurement that can be measured accurately using that instrument. To calculate the least count of a vernier caliper, we need to determine the difference between one main scale division and one vernier scale division.
Conversion to cm:
To convert the least count from mm to cm, we need to divide it by 10.
Calculations:
1. Determine the length of one main scale division:
- The main scale reading is 35 divisions.
- Each main scale division is equal to 1 mm.
- Therefore, the length of one main scale division is 35 mm.
2. Determine the length of one vernier scale division:
- According to the given information, 19 divisions of the main scale are equal in length to 20 divisions of the vernier scale.
- Therefore, the length of 20 vernier scale divisions is equal to 19 main scale divisions.
- The length of one vernier scale division is equal to (35 mm / 19) * 20.
3. Determine the difference between one main scale division and one vernier scale division:
- The length of one main scale division is 35 mm.
- The length of one vernier scale division is (35 mm / 19) * 20.
- The difference between one main scale division and one vernier scale division is 35 mm - (35 mm / 19) * 20.
4. Convert the difference to cm (least count):
- Divide the difference by 10 to convert it from mm to cm.
- Therefore, the least count is (35 mm - (35 mm / 19) * 20) / 10 cm.
Simplification:
To simplify the expression, we can use the fact that 1 mm is equal to 0.1 cm.
Final Calculation:
- The least count is (35 - (35 / 19) * 20) / 10 cm.
- Simplifying further, the least count is (35 - 36.8421) / 10 cm.
- The least count is -1.8421 / 10 cm.
- Finally, the least count is -0.18421 cm.
Correcting the Answer:
It seems that there was a mistake in the calculation or the given answer. The correct least count should be positive, as it represents the smallest measurement that can be accurately measured. Therefore, the correct least count is 0.18421 cm, which can be rounded to 0
Introduction:
Vernier calipers are precision measuring instruments used to measure lengths with high accuracy. They consist of a main scale and a vernier scale, which work together to provide precise measurements.
Given Information:
- The main scale is calibrated in mm (millimeters).
- 19 divisions of the main scale are equal in length to 20 divisions of the vernier scale.
- The main scale reading is 35 divisions.
- The 4th division of the vernier scale coincides with a main scale division.
Calculating the Least Count:
The least count of a measuring instrument is the smallest measurement that can be measured accurately using that instrument. To calculate the least count of a vernier caliper, we need to determine the difference between one main scale division and one vernier scale division.
Conversion to cm:
To convert the least count from mm to cm, we need to divide it by 10.
Calculations:
1. Determine the length of one main scale division:
- The main scale reading is 35 divisions.
- Each main scale division is equal to 1 mm.
- Therefore, the length of one main scale division is 35 mm.
2. Determine the length of one vernier scale division:
- According to the given information, 19 divisions of the main scale are equal in length to 20 divisions of the vernier scale.
- Therefore, the length of 20 vernier scale divisions is equal to 19 main scale divisions.
- The length of one vernier scale division is equal to (35 mm / 19) * 20.
3. Determine the difference between one main scale division and one vernier scale division:
- The length of one main scale division is 35 mm.
- The length of one vernier scale division is (35 mm / 19) * 20.
- The difference between one main scale division and one vernier scale division is 35 mm - (35 mm / 19) * 20.
4. Convert the difference to cm (least count):
- Divide the difference by 10 to convert it from mm to cm.
- Therefore, the least count is (35 mm - (35 mm / 19) * 20) / 10 cm.
Simplification:
To simplify the expression, we can use the fact that 1 mm is equal to 0.1 cm.
Final Calculation:
- The least count is (35 - (35 / 19) * 20) / 10 cm.
- Simplifying further, the least count is (35 - 36.8421) / 10 cm.
- The least count is -1.8421 / 10 cm.
- Finally, the least count is -0.18421 cm.
Correcting the Answer:
It seems that there was a mistake in the calculation or the given answer. The correct least count should be positive, as it represents the smallest measurement that can be accurately measured. Therefore, the correct least count is 0.18421 cm, which can be rounded to 0
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The main scale of a vernier callipers is calibrated in mm and 19 divisions of main scale are equal in length to 20 divisions of vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and 4th division of vernier scale coinsides with a main scale division. Find:(i). Least count(in cm)Correct answer is '0.005'. Can you explain this answer?
Question Description
The main scale of a vernier callipers is calibrated in mm and 19 divisions of main scale are equal in length to 20 divisions of vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and 4th division of vernier scale coinsides with a main scale division. Find:(i). Least count(in cm)Correct answer is '0.005'. 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 main scale of a vernier callipers is calibrated in mm and 19 divisions of main scale are equal in length to 20 divisions of vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and 4th division of vernier scale coinsides with a main scale division. Find:(i). Least count(in cm)Correct answer is '0.005'. 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 main scale of a vernier callipers is calibrated in mm and 19 divisions of main scale are equal in length to 20 divisions of vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and 4th division of vernier scale coinsides with a main scale division. Find:(i). Least count(in cm)Correct answer is '0.005'. Can you explain this answer?.
The main scale of a vernier callipers is calibrated in mm and 19 divisions of main scale are equal in length to 20 divisions of vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and 4th division of vernier scale coinsides with a main scale division. Find:(i). Least count(in cm)Correct answer is '0.005'. 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 main scale of a vernier callipers is calibrated in mm and 19 divisions of main scale are equal in length to 20 divisions of vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and 4th division of vernier scale coinsides with a main scale division. Find:(i). Least count(in cm)Correct answer is '0.005'. 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 main scale of a vernier callipers is calibrated in mm and 19 divisions of main scale are equal in length to 20 divisions of vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and 4th division of vernier scale coinsides with a main scale division. Find:(i). Least count(in cm)Correct answer is '0.005'. Can you explain this answer?.
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