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NEET
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NEET
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Physics
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Experimental Physics

NEET · Physics · Experimental Physics

A screw gauge has a pitch of 1 mm and 100 divisions on its circular...

A screw gauge has a pitch of 1 mm1\text{ mm} and 100100 divisions on its circular scale. When its jaws are fully closed, the zero of the circular scale is 44 divisions above the reference line. While measuring the diameter of a wire, the main scale reading is 2 mm2\text{ mm} and the circular scale reading is 4545 divisions. The true diameter of the wire is:

Options

  1. A2.41 mm2.41\text{ mm}
  2. B2.49 mm2.49\text{ mm}
  3. C2.45 mm2.45\text{ mm}
  4. D2.85 mm2.85\text{ mm}

Correct answer

B. 2.49 mm2.49\text{ mm}

Step-by-step solution

Least count (LC) of the screw gauge is:
LC=PitchNumber of circular scale divisions\text{LC} = \dfrac{\text{Pitch}}{\text{Number of circular scale divisions}}
LC=1 mm100=0.01 mm\text{LC} = \dfrac{1\text{ mm}}{100} = 0.01\text{ mm}

Since the zero of the circular scale is above the reference line when the jaws are closed, the screw gauge has a negative zero error.
Zero error=−4×0.01 mm=−0.04 mm\text{Zero error} = -4 \times 0.01\text{ mm} = -0.04\text{ mm}

The observed reading for the wire's diameter is:
Observed Reading=MSR+(CSR×LC)\text{Observed Reading} = \text{MSR} + (\text{CSR} \times \text{LC})
Observed Reading=2 mm+(45×0.01 mm)=2.45 mm\text{Observed Reading} = 2\text{ mm} + (45 \times 0.01\text{ mm}) = 2.45\text{ mm}

The true reading is obtained by subtracting the zero error from the observed reading:
True Reading=Observed Reading−Zero error\text{True Reading} = \text{Observed Reading} - \text{Zero error}
True Reading=2.45 mm−(−0.04 mm)=2.49 mm\text{True Reading} = 2.45\text{ mm} - (-0.04\text{ mm}) = 2.49\text{ mm}

Answer: 2.49 mm2.49\text{ mm}
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