In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main

Question

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division $=0.05 \mathrm{~mm}$, then the least count of the vernier callipers is $\_\_\_\_$ mm.

Professor PC Thomas Classes · Answer

We are given that 50 Vernier Scale Divisions (VSD) correspond to 48 Main Scale Divisions (MSD). Therefore, $1 	ext{ VSD} = \frac{48}{50} 	ext{ MSD}$. The Least Count (LC) of a vernier caliper is defined as the difference between one MSD and one VSD. $LC = 1 	ext{ MSD} - 1 	ext{ VSD} = 1 	ext{ MSD} - \frac{48}{50} 	ext{ MSD} = \frac{2}{50} 	ext{ MSD} = \frac{1}{25} 	ext{ MSD}$. Given that $1 	ext{ MSD} = 0.05 	ext{ mm}$, the least count is $LC = \frac{1}{25} 	imes 0.05 	ext{ mm} = 0.002 	ext{ mm}$.