One main scale division of a vernier callipers is 'a' cm and nth division of the vernier scale coincide with (n – 1)th division of the main scale.
Question:
One main scale division of a vernier callipers is ' $\mathrm{a}$ ' $\mathrm{cm}$ and $\mathrm{n}^{\text {th }}$ division of the vernier scale coincide with $(\mathrm{n}-1)^{\text {th }}$ division of the main scale. The least count of the callipers in $\mathrm{mm}$ is :
$\frac{10 n a}{(n-1)}$
$\frac{10 a}{(n-1)}$
$\left(\frac{\mathrm{n}-1}{10 \mathrm{n}}\right) \mathrm{a}$
$\frac{10 a}{n}$
Correct Option: , 4
Solution:
$(\mathrm{n}-1) \mathrm{a}=\mathrm{n}\left(\mathrm{a}^{\prime}\right)$
$a^{\prime}=\frac{(n-1) a}{n}$
$\therefore$ L.C. $=1 \mathrm{MSD}-1 \mathrm{VSD}$
$=\left(a-a^{\prime}\right) c m$
$=a-\frac{(n-1) a}{n}$
$=\frac{n a-n a+a}{n}=\frac{a}{n} \mathrm{~cm}$
$=\left(\frac{10 \mathrm{a}}{\mathrm{n}}\right) \mathrm{mm}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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