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10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division o…

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10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

[JEE Main 2024, 1 Feb (Shift 1)]

a

\(
\frac{1}{2}
\)

b

\(
\frac{5}{11}
\)

c

\(
\frac{50}{11}
\)

d

\(
\frac{10}{11}
\)

✓ Correct answer: b)

\(
\frac{5}{11}
\)

Explanation

\begin{equation}
\begin{aligned}
& \text { Given: } 10 \mathrm{MSD}=11 \mathrm{VSD} \\
& \Rightarrow 1 \mathrm{VSD}=\frac{10}{11} \mathrm{MSD} \\
& \text { As, } \mathrm{LC}=1 \mathrm{MSD}-1 \mathrm{VSD} \\
& =1 \mathrm{MSD}-\frac{10}{11} \mathrm{MSD}=\frac{1 \mathrm{MSD}}{11} \\
& =\frac{5}{11} \text { units }
\end{aligned}
\end{equation}

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