Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Units and Measurements question

2020 · 6 Sep · Shift 1 · Q56
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Units and Measurements
  5. /2020 · 6 Sep · Shift 1 · Q56

Units and Measurements question

2020 · 6 Sep · Shift 1 · Q56

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5mm is noticed on the pitch scale. The nature of zero error involved and the least count of the screw gauge, are respectively :
  1. A
    Positive, 0.1 mm
  2. B
    Positive, 0.1 μ\muμ m
  3. C
    Positive, 10 μ\muμ m
  4. D
    Negative, 2 μ\muμ m
View written solutionFree

Correct answer: C

  1. Find the pitch of the screw gauge

One complete rotation causes a linear displacement of 0.5 mm0.5\,\text{mm}0.5mm on the pitch scale.

So, the pitch is:

Pitch=0.5 mm\text{Pitch} = 0.5\,\text{mm}Pitch=0.5mm
  1. Find the least count

The circular scale has 505050 divisions.

Least count is given by:

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​

Thus,

LC=0.5 mm50=0.01 mm\text{LC} = \frac{0.5\,\text{mm}}{50} = 0.01\,\text{mm}LC=500.5mm​=0.01mm

Now convert to micrometre:

0.01 mm=10 μm0.01\,\text{mm} = 10\,\mu\text{m}0.01mm=10μm

So, the least count is 10 μm10\,\mu\text{m}10μm.

  1. Determine the nature of zero error

The statement says:

the circular scale is 4 units ahead of the pitch scale marking, prior to use.

When the circular scale zero is ahead of the reference line on the pitch scale, the screw gauge shows a reading even when it should read zero. This corresponds to a positive zero error.

Thus, the zero error is positive.

  1. Check options
  • A: Positive, 0.1 mm0.1\,\text{mm}0.1mm ❌
  • B: Positive, 0.1 μm0.1\,\mu\text{m}0.1μm ❌
  • C: Positive, 10 μm10\,\mu\text{m}10μm ✅
  • D: Negative, 2 μm2\,\mu\text{m}2μm ❌

Hence, the correct option is C.

PreviousNext

More from Units and Measurements

  • The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is (100x​) %. If the relative errors in measuring the mass and the…2020 · Numerical
  • A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm, 5.65 mm. The average of these four readings is 5.5375 mm and the…2020 · MCQ
  • The dimension of 2μ0​B2​, where B is magnetic field and μ0​ is the magnetic permeability of vacuum, is :2020 · MCQ
  • The dimension of stopping potential V0 in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :2020 · MCQ
  • 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 :2020 · MCQ
  • A quantity f is given by f=Ghc5​​ where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :2020 · MCQ
  • For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i) A1 = 24.36, B1 = 0.0724, C1 = 256.2 (ii) A2 = 24.44, B2 = 16.082, C2 = 240.2 (iii) A3 = 25.2, B3 = 19.2812, C3 =…2020 · MCQ
  • In SI units, the dimensions of μ0​∈0​​​ is :2019 · MCQ