Definition
Measurement of length with a vernier callipers
Measurement of length with a vernier callipers:
1. Find the least count and zero error of the vernier callipers.
2. Move the jaw J2 away from the jaw J1 and place the object to be measured, between the jaws J1 and J2. Move the jaw J2 towards the jaw J1 till it touches the object. Tighten the screw S to fix the vernier scale in its position.
3. Note the main scale reading.
4. Note that division p on vernier scale which coincides or is in line with any division of the main scale. Multiply this vernier division p with the least count. This is the vernier scale reading. i.e., Vernier scale reading = p L.C.
5. Add the vernier scale reading to the main scale reading. This gives the observed length.
1. Find the least count and zero error of the vernier callipers.
2. Move the jaw J2 away from the jaw J1 and place the object to be measured, between the jaws J1 and J2. Move the jaw J2 towards the jaw J1 till it touches the object. Tighten the screw S to fix the vernier scale in its position.
3. Note the main scale reading.
4. Note that division p on vernier scale which coincides or is in line with any division of the main scale. Multiply this vernier division p with the least count. This is the vernier scale reading. i.e., Vernier scale reading = p L.C.
5. Add the vernier scale reading to the main scale reading. This gives the observed length.
Definition
Pitch of a screw
The pitch of a screw is the distance moved along its axis by the screw in one complete rotation of its head.
Definition
Least count of a screw
The least count of a screw is the distance moved along the axis by it in rotating the circular scale by one division.
Definition
Principle of Screw gauge
The screw gauge works under the principle of the screw. When a screw is rotated in a nut, the distance moved by the tip of the screw is directly proportional to the number of rotations.
Definition
Construction of screw gauge
The Screw Gauge is an instrument to measure the dimensions of very small objects upto 0.01 mm.The Screw Gauge consists of aU shaped metal frame.A hollow cylinder is attached to one end of the frame.
Grooves are cut on the inner surface of the cylinder through which a screw passes. On the cylinder parallel to the axis of the screw a scale is graduated in millimeter called Pitch Scale.
One end of the screw is attached to a sleeve. The head of the sleeve is divided into 100 divisions called the Head Scale. The other end of the screw has a plane surface (S1 ). A stud (S2 ) is attached to the other end of the frame, just opposite the tip of the screw. The screw head is provided with a Ratchat arrangement (safety device) to prevent the user from exerting undue pressure.
Grooves are cut on the inner surface of the cylinder through which a screw passes. On the cylinder parallel to the axis of the screw a scale is graduated in millimeter called Pitch Scale.
One end of the screw is attached to a sleeve. The head of the sleeve is divided into 100 divisions called the Head Scale. The other end of the screw has a plane surface (S1 ). A stud (S2 ) is attached to the other end of the frame, just opposite the tip of the screw. The screw head is provided with a Ratchat arrangement (safety device) to prevent the user from exerting undue pressure.
Definition
Measurement of length in a screw gauge
The attached figure shows the measurement apparatus of a screw gauge. Steps to be taken for getting the correct reading are:
1. Find the zero error of the screw gauge, Z.
2. Note the main scale reading(M) and the circular scale reading (C). Hence, the reading is M+Cp where p is the least count.
3. Adjust for zero error.
1. Find the zero error of the screw gauge, Z.
2. Note the main scale reading(M) and the circular scale reading (C). Hence, the reading is M+Cp where p is the least count.
3. Adjust for zero error.
Formula
Positive and negative zero error in screw gauge
Zero Error of a Screw Gauge:
When the plane surface of the screw and the opposite plane stud on the frame are brought into contact, if the zero of the head scale coincides with the pitch scale axis, there is no zero error.
Positive Zero:
Error When the plane surface of the screw and the opposite plane stud on the frame are brought into contact, if the zero of the head scale lies below the pitch scale axis, the zero error is positive.For example the 5th division of the head scale coincides with the pitch scale axis, then the zero error is positive.
and the Zero Correction
Negative Zero Error:
When the plane surface of the screw and the opposite plane stud on the frame are brought into contact, if the Zero of the head scale lies above the pitch scale axis,the zero error is negative.For example the 5th division coincides with the pitch scale axis, then the zero error is negative and is given by:
and the Zero Correction
When the plane surface of the screw and the opposite plane stud on the frame are brought into contact, if the zero of the head scale coincides with the pitch scale axis, there is no zero error.
Positive Zero:
Error When the plane surface of the screw and the opposite plane stud on the frame are brought into contact, if the zero of the head scale lies below the pitch scale axis, the zero error is positive.For example the 5th division of the head scale coincides with the pitch scale axis, then the zero error is positive.
and the Zero Correction
Negative Zero Error:
When the plane surface of the screw and the opposite plane stud on the frame are brought into contact, if the Zero of the head scale lies above the pitch scale axis,the zero error is negative.For example the 5th division coincides with the pitch scale axis, then the zero error is negative and is given by:
and the Zero Correction
Definition
Calculating zero error in screw guage
The attached diagram shows cases of zero error in a screw guage.
Case (a): No zero-error
Case (b): Positive zero-error of 2 circular scale division. Positive zero-error correction is done by subtracting the positive zero-error from the actual reading.
Case (c): Negative zero-error of 4 circular scale division. Negative zero-error correction is done by adding the negative zero-error from the actual reading.
Case (a): No zero-error
Case (b): Positive zero-error of 2 circular scale division. Positive zero-error correction is done by subtracting the positive zero-error from the actual reading.
Case (c): Negative zero-error of 4 circular scale division. Negative zero-error correction is done by adding the negative zero-error from the actual reading.
Formula
Finding diameter of a thin wire using Screw gauge
Determine the Pitch, the Least Count and the Zero Error of the Screw Gauge.
Place the wire between the two studs.
Rotate the head until the wire is held firmly but not tightly, with the help of ratchet.
Note the reading on the pitch scale crossed by the head scale () and the head scale division that coincides with the pitch scale axis ().
The diameter of the wire is given by:
Repeat the experiment for different portions of the wire.
Tabulate the readings.
The average of the last column reading gives the diameter of the wire.
For example :Consider a wire of diameter nearly ,if measured from screw gauge having negative zero error and ,can found out to be from screw gauge.(Refer the table given.)
Definition
Errors in measurement of Physical Quantities
Any measurement made with a measuring device is approximate. If you measure the same object two different times, the two measurements may not be exactly the same. The difference between two measurements is called an error. The error in measurement is a mathematical way to show the uncertainty in the measurement. It is the difference between the result of the measurement and the true value.
Types of errors:
Types of errors:
- Systematic errors: The systematic errors are those errors that tend to be in one direction, either positive or negative.
- Instrumental errors
- Imperfection in experimental technique or procedure
- Personal Errors
- Random errors: These are the errors which occur irregularly and hence are random with respect to sign and size. These can arise due to random and unpredictable fluctuations in experimental conditions.
- Least count error: The least count error is the error associated with the resolution of the instrument.
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