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Units and Measurements question

2021 · 27 Jul · Shift 1 · Q65
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Units and Measurements question

2021 · 27 Jul · Shift 1 · Q65

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm. Reason R : Least Count = PitchTotal divisions on circular scale{{Pitch} \over {Total\,divisions\,on\,circular\,scale}}TotaldivisionsoncircularscalePitch​ In the light of the above statements, choose the most appropriate answer from the options given below :
  1. A
    A is not correct but R is correct.
  2. B
    Both A and R are correct and R is the correct explanation of A.
  3. C
    A is correct but R is not correct.
  4. D
    Both A and R are correct and R is NOT the correct explanation of A.
View written solutionFree

Correct answer: A

  1. Given data

    • In 5 complete rotations, the screw advances on the main scale by 5 mm5\ \text{mm}5 mm.
    • Total divisions on circular scale =50= 50=50.

  2. Find the pitch Pitch is the distance moved in one complete rotation. Pitch=5 mm5=1 mm\text{Pitch} = \frac{5\ \text{mm}}{5} = 1\ \text{mm}Pitch=55 mm​=1 mm

  3. Use the formula for least count For a screw gauge, Least Count=PitchNumber of divisions on circular scale\text{Least Count} = \frac{\text{Pitch}}{\text{Number of divisions on circular scale}}Least Count=Number of divisions on circular scalePitch​ Therefore, L.C.=1 mm50=0.02 mm\text{L.C.} = \frac{1\ \text{mm}}{50} = 0.02\ \text{mm}L.C.=501 mm​=0.02 mm

  4. Convert into cm Since 1 mm=0.1 cm1\ \text{mm} = 0.1\ \text{cm}1 mm=0.1 cm, 0.02 mm=0.002 cm0.02\ \text{mm} = 0.002\ \text{cm}0.02 mm=0.002 cm

  5. Check Assertion A Assertion says least count is 0.001 cm0.001\ \text{cm}0.001 cm. But actual least count is 0.002 cm0.002\ \text{cm}0.002 cm So, Assertion A is incorrect.

  6. Check Reason R The reason states: Least Count=PitchTotal divisions on circular scale\text{Least Count} = \frac{\text{Pitch}}{\text{Total divisions on circular scale}}Least Count=Total divisions on circular scalePitch​ This is the correct formula. So, Reason R is correct.

  7. Choose the correct option

    • A is not correct
    • R is correct

    Hence, the correct option is: A\boxed{\text{A}}A​

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