Question

The Vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, calculate the minimum inaccuracy in the measurement of distance.

Answer 1

Step: 1 Find the value of 1VSD.

Diagram of vernier scale is as shown below:


50 division of Vernier scale which coincide with 49 Main scale divisions.

50 VSD = 49 MSD

$1MSD=\frac{50}{49}VSDor1VSD=\frac{49}{50}MSD$

Where, MSD = Main scale division and VSD = Vernier scale division.

Step: 2 Find minimum inaccuracy.

We know that
Minimum inaccuracy = Vernier constant
= $1MSD-1VSD$
= $1MSD-\frac{49}{50}MSD$
= $\frac{1}{50}MSD$

It is given in the problem that $1MSD=0.5mm$
Hence, minimum inaccuracy = $\frac{1}{50}\times 0.5mm$
= $\frac{1}{100}$

= 0.01 mm

Final Answer: 0. 01 mm