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In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree (=05°), then the least count of the instrument is
  • a)
    one m inute
  • b)
    half minute
  • c)
    one degree
  • d)
    half degree
Correct answer is option 'A'. Can you explain this answer?
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Understanding the Instrument
In this experiment, we are using a measuring instrument that consists of a main scale and a vernier scale. The relationship between the two scales is crucial for determining the least count.
Divisions of Scales
- The main scale has 29 divisions that coincide with 30 divisions of the vernier scale.
- The smallest division of the main scale is given as half a degree (0.5 degrees).
Calculating the Value of One Vernier Division
To find the least count, we first need to understand the value of one division on the vernier scale.
- The total length of 29 main scale divisions = 29 * 0.5 degrees = 14.5 degrees.
- Since this length corresponds to 30 divisions of the vernier scale, the value of one vernier division can be calculated as:
Value of one vernier division = Total length of 29 main divisions / Number of vernier divisions
= 14.5 degrees / 30 = 0.4833 degrees (approximately).
Calculating the Least Count
Now, the least count (LC) of the instrument can be defined as:
- Least Count (LC) = Value of one main scale division - Value of one vernier scale division.
Substituting the values:
- Value of one main scale division = 0.5 degrees
- Value of one vernier division = 0.4833 degrees
Thus,
- LC = 0.5 degrees - 0.4833 degrees = 0.0167 degrees.
Converting to Minutes
Since 1 degree = 60 minutes:
- 0.0167 degrees = 0.0167 * 60 = 1 minute.
Conclusion
Therefore, the least count of the instrument is one minute, confirming that the correct answer is option 'A'.
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Vernier calipers:Vernier calipers are used to measure the thickness of thin plates, diameters of small cylinders etc. It has two scales–one main scale and a Vernier scale, which slides along the main scale. The main scale and Vernier scale are divided into small divisions though of different magnitudes. The difference in the magnitude of one main scale division (M.S.D.) and one vernier scale division (V.S.D.) is called the least count of the instrument, as it is the smallest distance that can be measured using the instrument. It is also known as vernier constant. Least count may also be defined as:When the jaws of vernier calipers touch each other, the zero of the Vernier should coincide with the zero of the main scale. If it is not so, then the instrument is said to have zero error. Zero error may be positive or negative, depending upon whether the zero of the vernier scale lies to the right or to the left of the zero of the main scale.A vernier callipers has vernier divisions = 10 and least count = 0.2 mm. What is the smallest distance can measured by this instrument?

Vernier calipers:Vernier calipers are used to measure the thickness of thin plates, diameters of small cylinders etc. It has two scales–one main scale and a Vernier scale, which slides along the main scale. The main scale and Vernier scale are divided into small divisions though of different magnitudes. The difference in the magnitude of one main scale division (M.S.D.) and one vernier scale division (V.S.D.) is called the least count of the instrument, as it is the smallest distance that can be measured using the instrument. It is also known as vernier constant. Least count may also be defined as:When the jaws of vernier calipers touch each other, the zero of the Vernier should coincide with the zero of the main scale. If it is not so, then the instrument is said to have zero error. Zero error may be positive or negative, depending upon whether the zero of the vernier scale lies to the right or to the left of the zero of the main scale.The least count of the instrument when 1MSD = 0.1 cm and number of vernier scale division = 10 is

Vernier calipers:Vernier calipers are used to measure the thickness of thin plates, diameters of small cylinders etc. It has two scales–one main scale and a Vernier scale, which slides along the main scale. The main scale and Vernier scale are divided into small divisions though of different magnitudes. The difference in the magnitude of one main scale division (M.S.D.) and one vernier scale division (V.S.D.) is called the least count of the instrument, as it is the smallest distance that can be measured using the instrument. It is also known as vernier constant. Least count may also be defined as:When the jaws of vernier calipers touch each other, the zero of the Vernier should coincide with the zero of the main scale. If it is not so, then the instrument is said to have zero error. Zero error may be positive or negative, depending upon whether the zero of the vernier scale lies to the right or to the left of the zero of the main scale.Which of the following figures has no zero error?

Vernier calipers:Vernier calipers are used to measure the thickness of thin plates, diameters of small cylinders etc. It has two scales–one main scale and a Vernier scale, which slides along the main scale. The main scale and Vernier scale are divided into small divisions though of different magnitudes. The difference in the magnitude of one main scale division (M.S.D.) and one vernier scale division (V.S.D.) is called the least count of the instrument, as it is the smallest distance that can be measured using the instrument. It is also known as vernier constant. Least count may also be defined as:When the jaws of vernier calipers touch each other, the zero of the Vernier should coincide with the zero of the main scale. If it is not so, then the instrument is said to have zero error. Zero error may be positive or negative, depending upon whether the zero of the vernier scale lies to the right or to the left of the zero of the main scale.Which figure shows positive zero error and which one shows positive zero error?

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In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree (=05°), then the least count of the instrument isa)one m inuteb)half minutec)one degreed)half degreeCorrect answer is option 'A'. Can you explain this answer?
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