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Units and Measurements question

2011 · Shift 0 · Q79
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Units and Measurements question

2011 · Shift 0 · Q79

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above date is:
  1. A
    0.052 cm
  2. B
    0.026 cm
  3. C
    0.005 cm
  4. D
    0.52 cm
View written solutionFree

Correct answer: A

  1. Find the least count of the screw gauge

Given:

  • 1 mm1\,\text{mm}1mm on the main scale corresponds to 100100100 divisions on the circular scale.

So, the value of 111 circular scale division is:

Least count=1 mm100=0.01 mm\text{Least count} = \frac{1\,\text{mm}}{100} = 0.01\,\text{mm}Least count=1001mm​=0.01mm
  1. Use the screw gauge reading formula

The total reading is:

Reading=Main scale reading+(Circular scale reading×Least count)\text{Reading} = \text{Main scale reading} + (\text{Circular scale reading} \times \text{Least count})Reading=Main scale reading+(Circular scale reading×Least count)

Given:

  • Main scale reading =0 mm= 0\,\text{mm}=0mm
  • Circular scale reading =52= 52=52

Thus,

Reading=0+(52×0.01 mm)=0.52 mm\text{Reading} = 0 + (52 \times 0.01\,\text{mm}) = 0.52\,\text{mm}Reading=0+(52×0.01mm)=0.52mm
  1. Convert into cm

Since:

1 cm=10 mm1\,\text{cm} = 10\,\text{mm}1cm=10mm

So,

0.52 mm=0.5210 cm=0.052 cm0.52\,\text{mm} = \frac{0.52}{10}\,\text{cm} = 0.052\,\text{cm}0.52mm=100.52​cm=0.052cm
  1. Match with the options

The diameter of the wire is:

0.052 cm0.052\,\text{cm}0.052cm

So the correct option is A.

  1. Comparison with stored correct answer

Stored correct answer: A

My derived answer: A

They match.

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