Question

# While measuring the length of a small rod using a vernier callipers, the difference between the observed length and the true length turned out to be 0.4 mm. When the jaws are made to touch each other, the 3rd division on the vernier scale coincides with a division on the main scale, then the least count of the callipers is:

A
0.133 cm
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B
1.33 cm
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C
0.00133 cm
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D
0.0133 cm
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Solution

## The correct option is D 0.0133 cmGiven: The difference between the observed length and the true length of a rod measured by the vernier callipers, Δl=0.4 mm=0.04 cm When the jaws touch each other, the 3rd division of the vernier scale coincides with a division on the main scale, i.e p=3. We know that, true length = observed length - zero error (with sign) ⟹ Observed length - true length = zero error (with sign) ⟹Δl= zero error (with sign) ⟹0.04=p×Least count ⟹Least count=0.04p ⟹Least count=0.043=0.0133 cm.

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