The main scale of a vernier calliper reads in $\mathrm{mm}$ and its vernier scale is divided into $8$ divisions, which coincides with $7$ divisions of the main scale. It was also observed that, when the two jaws are brought in contact, the zero of the vernier scale coincided with the zero of the main scale. The edge length of a cube is measured using this vernier calliper. The main scale reads $12 \mathrm{mm}$ and the $2^{\mathrm{nd}}$ division of the vernier scale coincides with the main scale. The edge length of the cube is $x \mathrm{mm}$. Find the value of $4x$.

What is the reading of micrometer screwgauge shown in figure :-

In a vernier calipers the main scale and the vernier scale are made up different materials. When the room temperature increases by $\mathrm{\Delta }T°\mathrm{C}$, it is found the reading of the instrument remains the same. Earlier it was observed that the front edge of the wooden rod placed for measurement crossed the $N^{\mathrm{th}}$ main scale division and $N+2 \mathrm{MSD}$  coincided with the $2^{\mathrm{nd}} \mathrm{VSD}$. Initially, $10 \mathrm{VSD}$  coincided with$9 \mathrm{MSD}$. If coefficient of linear expansion of the main scale is ${\alpha }_1$ and that of the vernier scale is ${\alpha }_2$ then what is the value of $\frac{{\alpha }_1}{{\alpha }_2}$ ? (Ignore the expansion of the rod on heating)