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NEET PHYSICSEasy

A Screw Gauge gives the following readings when used to measure the diameter of a wire. Main scale reading = 0.0 mm0.0\text{ mm} Circular scale reading = 52 divisions52\text{ divisions} Given that: 1 mm1\text{ mm} on the main scale corresponds to 100 divisions100\text{ divisions} of the circular scale. The diameter of the wire from the above data is:

A

0.026 cm0.026\text{ cm}

B

0.005 cm0.005\text{ cm}

C

0.52 cm0.52\text{ cm}

D

0.052 cm0.052\text{ cm}

Step-by-Step Solution

  1. Determine the Least Count (LC): The pitch of the screw gauge is given as 1 mm1\text{ mm}, and the total number of divisions on the circular scale is 100100. The least count is calculated as LC=PitchTotal circular divisions=1 mm100=0.01 mm\text{LC} = \frac{\text{Pitch}}{\text{Total circular divisions}} = \frac{1\text{ mm}}{100} = 0.01\text{ mm}.
  2. Calculate the Total Reading: The formula for the measurement is Total Reading=Main Scale Reading (MSR)+(Circular Scale Reading (CSR)×LC)\text{Total Reading} = \text{Main Scale Reading (MSR)} + (\text{Circular Scale Reading (CSR)} \times \text{LC}).
  3. Substitute the Values: Total Reading=0.0 mm+(52×0.01 mm)=0.52 mm\text{Total Reading} = 0.0\text{ mm} + (52 \times 0.01\text{ mm}) = 0.52\text{ mm}.
  4. Convert Units: The options are given in centimeters. To convert millimeters to centimeters, divide by 1010. Therefore, the diameter of the wire is 0.52 mm=0.052 cm0.52\text{ mm} = 0.052\text{ cm}.
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