In a Vernier calliper, when both jaws touch each other, zero or the Vernier scale shifts towards left and its 4th division coincides exactly with a certain division on main scale. If 50 Vernier scale divisions are equal to 49 main scale divisions and zero

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Solution

Q.
In a Vernier calliper, when both jaws touch each other, zero or the Vernier scale shifts towards left and its 4th division coincides exactly with a certain division on main scale. If 50 Vernier scale divisions are equal to 49 main scale divisions and zero error in the instrument is 0.4 mm, then how many main scale divisions are there in 1 cm [2024]

1 5

2 20

3 10

4 40

Ans.
(2)

$50$ $V S D = 49$ $M S D \Rightarrow 1$ $V S D = \frac{49}{50}$ $M S D$

$L C = 1$ $M S D - 1$ $V S D = 1$ $M S D - \frac{49}{50}$ $M S D = \frac{M S D}{50}$

$N o w, | z e r o e r r o r | = | 0 - 4 (L . C) |$

$0.04 = | - 4 (L . C) | \Rightarrow L . C . = 0.01 m m$

$Using (i) and (i i), \frac{M S D}{50} = 0.01$

$M S D = 0.5 mm \Rightarrow M S D = \frac{1 cm}{N}$

$N = \frac{1 cm}{0.5 mm} = \frac{100 mm}{5 mm} = 20$

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