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MCQEasyJEE 2026Vernier Calipers & Screw Gauge

JEE Physics 2026 Question with Solution

When both jaws of a vernier calipers touch each other, zero mark of the vernier scale is right to the zero mark of main scale. 44th mark on vernier scale coincides with a certain mark on the main scale. While measuring the length of a cylinder, observer observes 1515 divisions on main scale and 55th division of vernier scale coincides with a main scale division. Measured length of cylinder is _____ mm\text{mm}. (Least count of Vernier calliper = 0.1 mm0.1 \, \text{mm})

  • A

    15.415.4

  • B

    15.515.5

  • C

    15.915.9

  • D

    15.115.1

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given:

  • Zero mark of the vernier scale is to the right of the zero mark of the main scale.
  • 44th vernier division coincides when the jaws are closed.
  • Least count =0.1 mm= 0.1 \, \text{mm}
  • Main scale reading during measurement =15 mm= 15 \, \text{mm}
  • 55th vernier division coincides during measurement.

Find: The measured length of the cylinder.

Since the zero of the vernier scale lies to the right of the main scale zero, the zero error is positive.

Zero error=+4×0.1=+0.4 mm\text{Zero error} = +4 \times 0.1 = +0.4 \, \text{mm}

Now find the observed reading.

Main scale reading:

15 mm15 \, \text{mm}

Vernier scale reading:

5×0.1=0.5 mm5 \times 0.1 = 0.5 \, \text{mm}

Therefore, the observed reading is

15+0.5=15.5 mm15 + 0.5 = 15.5 \, \text{mm}

For positive zero error, the correction is subtracted from the observed reading.

Correct reading=15.5−0.4=15.1 mm\text{Correct reading} = 15.5 - 0.4 = 15.1 \, \text{mm}

Therefore, the measured length of the cylinder is 15.1 mm15.1 \, \text{mm}. The correct option is D.

Common mistakes

  • Treating the zero error as negative because the vernier zero is shifted. Here the vernier zero is to the right of the main scale zero, so the zero error is positive and must be subtracted, not added.

  • Using only the main scale reading and ignoring the vernier coincidence. The 55th vernier division contributes 0.5 mm0.5 \, \text{mm}, so the observed reading is not just 15 mm15 \, \text{mm}.

  • Subtracting the wrong zero correction by using the 55th coinciding division from the measurement instead of the 44th coinciding division from the closed-jaw condition. Zero error must be calculated from the closed-jaw reading only.

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