(C) $1$. Vernier Callipers: $1$ main scale division $(MSD)$ $= 1/8 \ cm = 0.125 \ cm$. Given $5$ $VSD$ $= 4$ $MSD$,so $1$ $VSD$ $= 4/5$ $MSD$ $= 0.8 \

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(C) $1$. Vernier Callipers: $1$ main scale division $(MSD)$ $= 1/8 \ cm = 0.125 \ cm$. Given $5$ $VSD$ $= 4$ $MSD$,so $1$ $VSD$ $= 4/5$ $MSD$ $= 0.8 \times 0.125 \ cm = 0.1 \ cm$. Least Count $(LC)$ $= 1$ $MSD$ $- 1$ $VSD$ $= 0.125 - 0.1 = 0.025 \ cm = 0.25 \ mm$.$2$. Screw Gauge: One rotation moves it by $2$ divisions on the linear scale. Let $1$ linear scale division $= x$. Pitch $P = 2x$. $LC$ $= P / 100 = 2x / 100 = x / 50$.$3$. Case $1$: Pitch $P = 2 \times$ $LC$ of Vernier $= 2 \times 0.25 \ mm = 0.5 \ mm$. Then $LC$ of screw gauge $= 0.5 \ mm / 100 = 0.005 \ mm$. (Option $B$ is correct).$4$. Case $2$: Linear scale division $x = 2 \times$ $LC$ of Vernier $= 2 \times 0.25 \ mm = 0.5 \ mm$. Then $LC$ of screw gauge $= x / 50 = 0.5 \ mm / 50 = 0.01 \ mm$. (Option $C$ is correct).

Class 11 Physics Units, Dimensions and Measurement Vernier Calipers, Micrometer screw gauge

Consider a Vernier callipers in which each $1 \ cm$ on the main scale is divided into $8$ equal divisions and a screw gauge with $100$ divisions on its circular scale. In the Vernier callipers,$5$ divisions of the Vernier scale coincide with $4$ divisions on the main scale and in the screw gauge,one complete rotation of the circular scale moves it by two divisions on the linear scale. Then:
$(A)$ If the pitch of the screw gauge is twice the least count of the Vernier callipers,the least count of the screw gauge is $0.01 \ mm$.
$(B)$ If the pitch of the screw gauge is twice the least count of the Vernier callipers,the least count of the screw gauge is $0.005 \ mm$.
$(C)$ If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers,the least count of the screw gauge is $0.01 \ mm$.
$(D)$ If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers,the least count of the screw gauge is $0.005 \ mm$.

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$(A, D)$
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$(C, D)$

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Units, Dimensions and Measurement

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Vernier Calipers, Micrometer screw gauge

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The length of a cylinder measured by a Vernier caliper is given by the following observations: $3.29 \, cm, 3.28 \, cm, 3.29 \, cm, 3.31 \, cm, 3.28 \, cm, 3.27 \, cm, 3.29 \, cm, 3.30 \, cm$. The most accurate length of the cylinder is ........ $cm$.

Easy

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$A$ plano-convex lens of unknown material and unknown focal length is given. With the help of a Spherometer,we can measure the,

EasyNEET 2020

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The one division of main scale of vernier callipers reads $1\,mm$ and $10$ divisions of Vernier scale is equal to the $9$ divisions on main scale. When the two jaws of the instrument touch each other the $zero$ of the Vernier lies to the right of $zero$ of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws,the $zero$ of the Vernier scale lies in between $4.1\,cm$ and $4.2\,cm$ and $6^{\text{th}}$ Vernier division coincides with a main scale division. The diameter of the bob will be $.............10^{-2}\,cm$

DifficultJEE MAIN 2022

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In a vernier callipers, $50$ vernier scale divisions are equal to $48$ main scale divisions. If one main scale division $= 0.05 \ mm$, then the least count of the vernier callipers is . . . . . . $mm$.

MediumJEE MAIN 2026

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Answer the following:
$(a)$ You are given a thread and a metre scale. How will you estimate the diameter of the thread?
$(b)$ $A$ screw gauge has a pitch of $1.0\; mm$ and $200$ divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale?
$(c)$ The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of $100$ measurements of the diameter expected to yield a more reliable estimate than a set of $5$ measurements only?

Medium

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The length of a cylinder measured by a Vernier caliper is given by the following observations: $3.29 \, cm, 3.28 \, cm, 3.29 \, cm, 3.31 \, cm, 3.28 \, cm, 3.27 \, cm, 3.29 \, cm, 3.30 \, cm$. The most accurate length of the cylinder is ........ $cm$.

$A$ plano-convex lens of unknown material and unknown focal length is given. With the help of a Spherometer,we can measure the,

In a vernier callipers, $50$ vernier scale divisions are equal to $48$ main scale divisions. If one main scale division $= 0.05 \ mm$, then the least count of the vernier callipers is . . . . . . $mm$.

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