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Units and Measurements question

2020 · 9 Jan · Shift 1 · Q56
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Units and Measurements question

2020 · 9 Jan · Shift 1 · Q56

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is :
  1. A
    0.001 mm
  2. B
    0.01 cm
  3. C
    0.02 mm
  4. D
    0.001 cm
View written solutionFree

Correct answer: D

  1. Find the pitch of the screw gauge
    Pitch = distance moved in one complete rotation.

Given:

  • In 666 rotations, the screw moves 3 mm3\text{ mm}3 mm.

So,

Pitch=3 mm6=0.5 mm\text{Pitch} = \frac{3\text{ mm}}{6} = 0.5\text{ mm}Pitch=63 mm​=0.5 mm
  1. Use the formula for least count
    Least count of a screw gauge is:
Least Count=PitchNumber of circular scale divisions\text{Least Count} = \frac{\text{Pitch}}{\text{Number of circular scale divisions}}Least Count=Number of circular scale divisionsPitch​

Given circular scale divisions =50= 50=50.

Thus,

Least Count=0.5 mm50=0.01 mm\text{Least Count} = \frac{0.5\text{ mm}}{50} = 0.01\text{ mm}Least Count=500.5 mm​=0.01 mm
  1. Convert to cm if needed
0.01 mm=0.001 cm0.01\text{ mm} = 0.001\text{ cm}0.01 mm=0.001 cm

because 1 mm=0.1 cm1\text{ mm} = 0.1\text{ cm}1 mm=0.1 cm.

  1. Match with the options
  • A: 0.001 mm0.001\text{ mm}0.001 mm ❌
  • B: 0.01 cm=0.1 mm0.01\text{ cm} = 0.1\text{ mm}0.01 cm=0.1 mm ❌
  • C: 0.02 mm0.02\text{ mm}0.02 mm ❌
  • D: 0.001 cm0.001\text{ cm}0.001 cm ✅

Therefore, the correct answer is Option D.

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