Question 36: Units , Dimensions and Error Analysis

Question

In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is $\_\_\_\_$ mm.
[Assume least count is 0.01 mm ]

Accepted Answer

The circular scale lies 3 divisions above the horizontal pitch line when the studs are in contact.
When the zero mark is above the reference line, the screw has been turned past the zero point. This indicates a negative zero error. The error corresponds to 3 divisions.
Hence, the zero error is,
$$\mathrm{E}_0=-(3 	imes 	ext { Least Count }) =-(3 	imes 0.01 \mathrm{~mm})=-0.03 \mathrm{~mm} $$
The observed reading is the sum of the Pitch Scale Reading (PSR) and the Circular Scale Reading (CSR) multiplied by the Least Count (LC).
The given Pitch Scale Reading (PSR) is 1 mm and the Circular Scale Reading (CSR) is 51
So, the observed reading $=\mathrm{PSR}+(\mathrm{CSR} 	imes \mathrm{LC})$
Observed Reading $=1 \mathrm{~mm}+(51 	imes 0.01 \mathrm{~mm})$
Observed Reading $=1 \mathrm{~mm}+0.51 \mathrm{~mm}$
Observed Reading $=1.51 \mathrm{~mm}$
To find the true thickness, we must subtract the zero error from the observed reading.
Correct Reading $=$ Observed Reading - Zero Error
Correct Reading $=1.51 \mathrm{~mm}-(-0.03 \mathrm{~mm})$
Correct Reading $=1.51 \mathrm{~mm}+0.03 \mathrm{~mm}$
Correct Reading $=1.54 \mathrm{~mm}$
Therefore, the correct thickness of the sheet is 1.54 mm.
Hence, the correct option is (A).

Answer

1.54

Answer

1.50

Answer

1.51

Answer

1.48

Units , Dimensions and Error Analysis

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