Least Count of Vernier Callipers and Screw Gauge Physics Notes
Least count of vernier callipers and screw gauge:
(A) Vernier callipers: It is a precision instrument that can be used to measure internal and external distances accurately.
Construction of vernier callipers:
1. Adjacent figure: A and B represents side jaws. They are used to measure the external diameter or width of an object. Here, A is a fixed Jaw and Bis a movable jaw. C and D represent inside jaws. They are used to measure the internal diameter of an object. Here, C is a fixed jaw and D is a movable jaw.
Vernier Callipers
2. Main scale: The main scale consists of a metalic steel strip graduated with the value of one division on it equal to 1 mm. It is generally 15 cm to 20 cm long. It carries the inner and outer measuring jaws. When the two jaws are in contact, the zero of the main scale and zero of the vernier scale should coincide. If both the zeros do not coinside, there will be a positive or a negative zero error.
3. Vernier scale: Vernier scale is a small movable scale which can slide along the main scale. It has 10 divisions marked on it, such that the total length of 10 divisions is equal to 9 mm. In other words, 10 vernier scale divisions coincide with nine main scale divisions.
Least count: Least count refers to the smallest distance that can be measured using an instrument. It indicates the degree of precision of an instrument.
The least count as the name suggests is the finest measurement you can take with the help of that vernier calliper. The least count (LC) of vernier scale is given as:
Least count = \(\frac{\text { Least count of main scale }}{\text { Number of divisions on vernier scale }}\)
Least count of the main scale: The main scale is callibrated in millimetres. To get the least count of the main scale, count the number of divisions on the main scale in 1 cm of it. Divide 1 cm into that much number of divisions; the value obtained is the least count 0 the mains scale in cm. For example, If there are 10 divisions is 1 cm of the main scale, its least count.
= \(\frac{1}{10}\) = 0.1 cm
Number of divisions on vernier scale: Count the number of divisions on the vernier scale. Use a magnifying glass if necessary. In most vernier caliper, the vernier scale has 10 divisions.
Thus, least count of vernier calliper
= \(\frac{0.1}{10}\) = 0.01 cm
Since the least count of the vernier calliper is 0.01 cm, it can be said that when measuring with the help of this vernier calliper, you can get an accuracy of 0.01 cm. They are extensively used to measure the internal and external diameters of tubes as well as dimensions of many more objects.
(B) The screw gauge: The screw gauge is an instrument used for measuring accurately the diameter of a thin wire or the thickness of a sheet of a metal. It consists of a U-shaped frame fitted with a screwed spindle which is attached to a thimble.
Screw Gauge
Parallel to the axis of the thimble, a scale graduated in mm is engraved, This is called the pitch scale. A sleeve is attached to the life head of the screw.
The head of the screw has a hatchet which avoids undue tightening of the screw. On the thimble, there is a circular scale known as the head scale which is divided into 50 or 100 equal parts.
A stud with a plane end surface calW the anvil is fixed on the ‘17’ frame exactly opposite to “the tip of the screw. When the tip of the screw is in contact with the anvil, usually, the zero of the head scale coincides with the zero of the pitch scale.
Pitch of the screw-gauge: The pitch of the screw-gauge is the distance moved by the spindle per revolution. To find out this, the distance advanced by the head scale over the pitch scale for a definite number of complete rotation of the screw is determined.
The pitch can be represented as:
Pitch of the screw = \(\frac{\text { Distance moved by screw }}{\text { No. of full rotations given }}\)…(1)
Least-count of the screw gauge:
The least count (LC) is the distance moved by the tip of the screw, when the screw is turned through 1 (one) division of the head scale.
The least count can be calculated using the formula:
Least count = \(\frac{\text { Pitch }}{\text { Total no. of divisions on the circular scale }}\) …(2)
Total no. of divisions on the circular scale
If the pitch of the screw is 1 mm and
If circular disc is divided into 100 equal parts,
Then L.C. = \(\frac{1}{100}\) = 0.01 mm = 0.001 cm