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 $0.4mm$. 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. $0.00133cm$
• B. $0.133cm$
• C. $1.33cm$
• D. $0.0133cm$

Answer 1

The correct option is D $0.0133cm$

Given:
The difference between the observed length and the true length of a rod measured by the vernier callipers, $\Delta l=0.4mm=0.04cm$
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)
$⟹\Delta l=$ zero error (with sign)
$⟹0.04=p\times \text{Least count}$
$⟹\text{Least count}=\frac{0.04}{p}$
$⟹\text{Least count}=\frac{0.04}{3}=0.0133cm$.