One main scale division of a vernier caliper is equal to m units. If n th division of main scale coincides with ( n +1) th division of vernier scale, the least count of the vernier caliper is:

Physics · Units, Dimensions & Error Analysis

JEE Main 2024 — 9 April, Shift 1 — Question 47

One main scale division of a vernier caliper is equal to $m$ units. If $\mathrm{n}^{\text {th }}$ division of main scale coincides with $(\mathrm{n}+1)^{\text {th }}$ division of vernier scale, the least count of the vernier caliper is:

Option A:
$\frac{\mathrm{n}}{(\mathrm{n}+1)}$
Option B:
$\frac{m}{(n+1)}$
Correct
Option C:
$\frac{1}{(n+1)}$
Option D:
$\frac{m}{n(n+1)}$

Answer: B

Step-by-step solution

$\mathrm{n} \operatorname{MSD}=(\mathrm{n}+1) \mathrm{VSD}$

$\Rightarrow 1 \mathrm{VSD}=\frac{\mathrm{n}}{\mathrm{n}+1} \mathrm{MSD}$

$\mathrm{L} \cdot \mathrm{C}=1 \mathrm{MSD}-1 \mathrm{VSD}$

$L \cdot C=m-m\left(\frac{n}{n+1}\right)$

$\mathrm{L} \cdot \mathrm{C}=\mathrm{m}\left(\frac{\mathrm{n}+1-\mathrm{n}}{\mathrm{n}+1}\right)$

$\Rightarrow \mathrm{L} \cdot \mathrm{C}=\left(\frac{\mathrm{m}}{\mathrm{n}+1}\right)$

Answer key and solution verified before publishing.

Practise Units, Dimensions & Error Analysis

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 9 April, Shift 1
Subject: Physics
Chapter: Units, Dimensions & Error Analysis
Topic: Vernier Calipers and Screw Gauge

The dimensional formula of latent heat is:

Answer: B

Step-by-step solution

Practise Units, Dimensions & Error Analysis

More Units, Dimensions & Error Analysis questions from this paper