The vernier scale of a travelling microscope has $50$ divisions which coincide with $49$ main scale divisions. If each main scale division is $0.5\, mm$, calculate the minimum inaccuracy in the measurement of distance.
The vernier scale of a travelling microscope has $50$ divisions which coincide with $49$ main scale divisions. If each main scale division is $0.5\, mm$, calculate the minimum inaccuracy in the measurement of distance.
$50 \mathrm{VSD}=49 \mathrm{MSD}$
$\therefore \quad \operatorname{lMSD}=\frac{50}{49} \mathrm{VSD}$
$\text { and } 1 \mathrm{VSD}=\frac{49}{50} \mathrm{MSD}$
Minimum inaccuracy $=1 \mathrm{MSD}-1 \mathrm{VSD}$
$=1 \mathrm{MSD}-\frac{49}{50} \mathrm{MSD}=\frac{1}{50} \mathrm{MSD}$
Now, $1 \mathrm{MSD}=0.5 \mathrm{~mm} \quad$ (given)
$\therefore$ Minimum inaccuracy,
$=\frac{1}{50} \times 0.5 \mathrm{~mm}=\frac{1}{100}=0.01 \mathrm{~mm}$
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