In a vernier calliper, when both jaws touch each other, zero of vernier scale shifts towards left an

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1.Units, Dimensions and Measurement

hard

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 $1 \mathrm{~cm}$ ?

A

$40$

B

$5$

C

$20$

D

$10$

(JEE MAIN-2024)

Solution

$4^{\text {th }}$ division coincides with $3^{\text {rd }}$ division then

$ 0.004 \mathrm{~cm}=4 \mathrm{VSD}-3 \mathrm{MSD}$

$49 \mathrm{MSD}=50 \mathrm{VSD}$

$1 \mathrm{MSD}=\frac{1}{\mathrm{~N}} \mathrm{~cm}$

$0.004=4\left\{\frac{49}{50} \mathrm{MSD}\right\}-3 \mathrm{MSD}$

$0.004=\left(\frac{196}{50}-3\right)\left(\frac{1}{\mathrm{~N}}\right)$

$\mathrm{N}=\frac{46}{50} \times \frac{1000}{4}=\frac{46 \times 1000}{200}=230$

Standard 11

Physics

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