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MCQEasyJEE 2024Vernier Calipers & Screw Gauge

JEE Physics 2024 Question with Solution

A spherometer has a circular base of radius 3.5 cm3.5 \, \text{cm}. The central screw moves 2 mm2 \, \text{mm} for every complete rotation. How many rotations should be given to the central screw to raise it from the base by 4.2 mm4.2 \, \text{mm}?

  • A

    33

  • B

    55

  • C

    66

  • D

    77

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: The central screw moves 2 mm2 \, \text{mm} in one complete rotation, and it has to be raised by 4.2 mm4.2 \, \text{mm}.

Find: The number of rotations required.

The solution states that the required rotations are calculated from the height increase per rotation.

Using the relation:

Number of rotations=required heightheight per rotation\text{Number of rotations} = \frac{\text{required height}}{\text{height per rotation}}

Substituting the given values:

Number of rotations=4.22=2.1\text{Number of rotations} = \frac{4.2}{2} = 2.1

The solution concludes with Final Answer: 33. Therefore, the correct option is A.

Common mistakes

  • Using the radius of the circular base in the calculation. It is not needed here because the question only depends on the screw movement per rotation. Use only the vertical rise per rotation.

  • Assuming the answer must come from direct geometry of a spherometer. This question is simpler: compare the required rise with the rise in one complete rotation.

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