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Units and Measurements question

2023 · 10 Apr · Shift 2 · Q55
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Units and Measurements question

2023 · 10 Apr · Shift 2 · Q55

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
In an experiment with vernier callipers of least count 0.1 mm0.1 \mathrm{~mm}0.1 mm, when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6th division of vernier scale coincides with the main scale division. While measuring the diameter of a spherical bob, the zero of vernier scale lies in between 3.2 cm3.2 \mathrm{~cm}3.2 cm and 3.3 cm3.3 \mathrm{~cm}3.3 cm marks, and 4th division of vernier scale coincides with the main scale division. The diameter of bob is measured as
  1. A
    3.18 cm3 .18 \mathrm{~cm}3.18 cm
  2. B
    3.22 cm3.22 \mathrm{~cm}3.22 cm
  3. C
    3.26 cm3.26 \mathrm{~cm}3.26 cm
  4. D
    3.25 cm3.25 \mathrm{~cm}3.25 cm
View written solutionFree

Correct answer: A

  1. Find the zero error

When the jaws are closed, the vernier zero lies to the right of the main scale zero. This means the zero error is positive.

Given:

  • Least count =0.1 mm=0.01 cm= 0.1\text{ mm} = 0.01\text{ cm}=0.1 mm=0.01 cm
  • 666th vernier division coincides

So, zero error

=6×0.1 mm=0.6 mm=0.06 cm= 6 \times 0.1\text{ mm} = 0.6\text{ mm} = 0.06\text{ cm}=6×0.1 mm=0.6 mm=0.06 cm

Thus, zero correction will be

−0.06 cm-0.06\text{ cm}−0.06 cm
  1. Find the observed reading

While measuring the bob:

  • Vernier zero lies between 3.2 cm3.2\text{ cm}3.2 cm and 3.3 cm3.3\text{ cm}3.3 cm
  • So main scale reading =3.2 cm= 3.2\text{ cm}=3.2 cm
  • 444th vernier division coincides

Vernier reading:

4×0.01 cm=0.04 cm4 \times 0.01\text{ cm} = 0.04\text{ cm}4×0.01 cm=0.04 cm

Observed reading:

3.2+0.04=3.24 cm3.2 + 0.04 = 3.24\text{ cm}3.2+0.04=3.24 cm
  1. Apply zero correction

Actual reading

=Observed reading+Zero correction= \text{Observed reading} + \text{Zero correction}=Observed reading+Zero correction =3.24−0.06=3.18 cm= 3.24 - 0.06 = 3.18\text{ cm}=3.24−0.06=3.18 cm
  1. Match with options

Therefore, the diameter of the bob is

3.18 cm\boxed{3.18\text{ cm}}3.18 cm​

So the correct option is A.

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