KCET · Physics · Experimental Physics
The Vernicr scale of a travelling microscope has 50 divisions which coincides with 49 main scale divisions. If each main scale division is \(0.5 \mathrm{~mm}\), then the least count of the microscope is
- A \(0.5 \mathrm{~mm}\)
- B \(0.01 \mathrm{~mm}\)
- C \(0.5 \mathrm{~cm}\)
- D \(0.01 \mathrm{~cm}\)
Answer & Solution
Correct Answer
(B) \(0.01 \mathrm{~mm}\)
Step-by-step Solution
Detailed explanation
Given, reading of 1 main scale division
\[
\begin{aligned}
& =0.5 \mathrm{~mm} \\
& \text { i.e. } \quad 1 \mathrm{MSD}=0.5 \mathrm{~mm} \\
& \text { According to given situation, } \\
& 50 \text { vernier scale division }=49 \text { main scale division } \\
& \Rightarrow 1 \text { vernier scale division (VSD) } \\
& =\frac{49}{50} \text { main scale division (MSD) } \\
& \therefore \text { Least count }=1 \mathrm{MSD}-1 \text { VSD } \\
& =1 \mathrm{MSD}-\frac{49}{50} \mathrm{MSD}=\frac{1}{50} \mathrm{MSD} \\
& =\frac{1}{50} \times 0.5=0.01 \mathrm{~mm} \\
&
\end{aligned}
\]
\[
\begin{aligned}
& =0.5 \mathrm{~mm} \\
& \text { i.e. } \quad 1 \mathrm{MSD}=0.5 \mathrm{~mm} \\
& \text { According to given situation, } \\
& 50 \text { vernier scale division }=49 \text { main scale division } \\
& \Rightarrow 1 \text { vernier scale division (VSD) } \\
& =\frac{49}{50} \text { main scale division (MSD) } \\
& \therefore \text { Least count }=1 \mathrm{MSD}-1 \text { VSD } \\
& =1 \mathrm{MSD}-\frac{49}{50} \mathrm{MSD}=\frac{1}{50} \mathrm{MSD} \\
& =\frac{1}{50} \times 0.5=0.01 \mathrm{~mm} \\
&
\end{aligned}
\]
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