In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line
Q. 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]
A. 1.54
B. 1.50
C. 1.51
D. 1.48
Correct Answer: 1.54

Explanation

Least count of the screw gauge is given as

$$ \text{LC} = 0.01 \text{ mm} $$

Given that the zero of the circular scale lies 3 divisions above the pitch line, hence there is a positive zero error.

Zero error is

$$ \text{Zero error} = +3 \times 0.01 = +0.03 \text{ mm} $$

Zero correction is equal in magnitude but opposite in sign, hence

$$ \text{Zero correction} = -0.03 \text{ mm} $$

Observed reading of the screw gauge is

$$ \text{Observed reading} = \text{Pitch scale reading} + (\text{Circular scale reading} \times \text{LC}) $$

$$ = 1 + (51 \times 0.01) $$

$$ = 1 + 0.51 = 1.51 \text{ mm} $$

Correct thickness of the sheet is obtained by applying zero correction:

$$ \text{Correct reading} = 1.51 - (-0.03) $$

$$ = 1.54 \text{ mm} $$

Therefore, the correct thickness of the sheet is

$$ \boxed{1.54 \text{ mm}} $$

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