Question

Which of the following is the most precise device for measuring length?

$\left(\text{A}\right)$ A vernier caliper with $20$ divisions on a sliding scale coinciding with $19$ main scale divisions.$(1\text{MSD}=1\text{mm})$

$\left(\text{B}\right)$ A screw gauge with $1\text{mm}$ pitch and $200$ divisions on a circular scale

Answer 1

To check the most precise device, we will find the least count in both the cases and whichever will have lesser value of the least count will be more precise.

For Vernier caliper :

$\text{Least count (LC)= 1 MSD (main scale division)- 1 VSD (vernier scale division)}$

Given,
$19\text{MSD}=20\text{VSD}$
Therefore,
$LC=1MSD-\frac{19}{20}MSD$
$LC=\frac{1}{20}MSD=\frac{1}{20}\text{mm}=\frac{1}{200}\text{cm}(1MSD=1\text{mm})$

For screw gauge :
$LC=\frac{\text{pitch}}{\text{no. of divisions on circular scale}}$

Given ,
pitch$=1\text{mm}$ and no. of divisions$=200$

$\Rightarrow LC=\frac{1}{\text{200}}\text{mm}=\frac{1}{\text{2000}}\text{cm}$

As we can see that,

$L{C}_{screw}<L{C}_{vernier}$

Hence, screw gauge is the most precise device among the two.

So, option $\left(\text{B}\right)$ is correct.