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In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{\text {th }}$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is $0.04 \mathrm{~mm}$ then how many main scale divisions are there in $1 \mathrm{~cm}$ ?
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Verified Answer
The correct answer is:
20
$\begin{aligned}
& 50 \mathrm{VSD}=49 \mathrm{MSD} \\
& 1 \mathrm{VSD}=\frac{49}{50} \mathrm{MSD} \\
& \mathrm{LC}=1 \mathrm{MSD}-1 \mathrm{VSD} \\
& \mathrm{LC}=1 \mathrm{MSD} \cdot \frac{49}{50} \mathrm{MSD}=\frac{\mathrm{MSD}}{50} \ldots . . . . . .(1) \\
& \text {Now, } | \text { zero error }|=| 0-4(\mathrm{~L} . \mathrm{C}) | \\
& 0.04=|-4(\mathrm{~L} . \mathrm{C})| \Rightarrow \mathrm{L} . \mathrm{C}=0.01 \mathrm{~mm} \\
& \mathrm{0 . 0 4}=|-\mathrm{4}(\mathrm{L} . \mathrm{C})| \Rightarrow \mathrm{L} . \mathrm{C} \ldots . . .(2) \\
& =\mathrm{0 . 0 1} \mathrm{mm}
\end{aligned}$
Using (1) and (2)
$\begin{aligned}
& \frac{M S D}{50}=0.01 \\
& M S D=0.5 \mathrm{~mm} \\
& M S D=\frac{1 \mathrm{~cm}}{\mathrm{~N}} \\
& \mathrm{~N}=\frac{1 \mathrm{~cm}}{0.5 \mathrm{~mm}}=\frac{100 \mathrm{~mm}}{5 \mathrm{~mm}} \\
& \mathrm{~N}=20
\end{aligned}$
& 50 \mathrm{VSD}=49 \mathrm{MSD} \\
& 1 \mathrm{VSD}=\frac{49}{50} \mathrm{MSD} \\
& \mathrm{LC}=1 \mathrm{MSD}-1 \mathrm{VSD} \\
& \mathrm{LC}=1 \mathrm{MSD} \cdot \frac{49}{50} \mathrm{MSD}=\frac{\mathrm{MSD}}{50} \ldots . . . . . .(1) \\
& \text {Now, } | \text { zero error }|=| 0-4(\mathrm{~L} . \mathrm{C}) | \\
& 0.04=|-4(\mathrm{~L} . \mathrm{C})| \Rightarrow \mathrm{L} . \mathrm{C}=0.01 \mathrm{~mm} \\
& \mathrm{0 . 0 4}=|-\mathrm{4}(\mathrm{L} . \mathrm{C})| \Rightarrow \mathrm{L} . \mathrm{C} \ldots . . .(2) \\
& =\mathrm{0 . 0 1} \mathrm{mm}
\end{aligned}$
Using (1) and (2)
$\begin{aligned}
& \frac{M S D}{50}=0.01 \\
& M S D=0.5 \mathrm{~mm} \\
& M S D=\frac{1 \mathrm{~cm}}{\mathrm{~N}} \\
& \mathrm{~N}=\frac{1 \mathrm{~cm}}{0.5 \mathrm{~mm}}=\frac{100 \mathrm{~mm}}{5 \mathrm{~mm}} \\
& \mathrm{~N}=20
\end{aligned}$
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