Question

Two identical triangular sets are used to measure the length of a rod. The division on the triangles are equally spaced. If the length of the rod is found to be $6.5\,mm$ then calculate the division length (in $mm)$

Answer 1

Suppose one division length is $l$ .
Then, size of main scale division, $AB=\frac{l}{cos \left(37 ^\circ \right)}=\frac{5 l}{4}$
Least count of the calliper will be,
$LC=1MSD-1VSD\Rightarrow LC=\frac{5 l}{4}-l=\frac{l}{4}$
The main scale reading is two and the third vernier scale is coinciding with the main scale.
So, length of the rod,
$6.5\,mm=2MSD+3LC\Rightarrow 6.5\,mm=2\frac{5 l}{4}+3\frac{l}{4}\Rightarrow l=2\,mm$