Question

The diagram below shows part of the main scale and vernier scale of a vernier callipers, which is used to measure the diameter of a metal ball. Find the least count and the radius of the ball.

• A. $0.01cm,2.18cm$
• B. $0.02cm,2.18cm$
• C. $0.01cm,2.17cm$
• D. None of these

Answer 1

The correct option is A $0.01cm,2.18cm$

Least count $,LC=1MSD-1VSD$

Here $10VSD=9MSD$ or $1VSD=\left(9/10\right)MSD$

Thus, $LC=(1-9/10)1MSD=1/10\times 0.1cm=0.01cm$ (as $1MSD=0.1cm$ from diagram)

From diagram, main scale reading, $MSR=4.3cm$ and vernier scale reading, $VSR=7$ (because division $7$ coincide with any line on main scale )

The diameter of the metal ball $=MSR+(VSR\times LC)=4.3+(7\times 0.01)=4.37cm$

Radius of the ball $=4.37/2=2.185cm=2.18cm$