Question

N divisions on the main scale of vernier callipers coincide with $(N+1)$ divisions on the vernier scale. If each division on the main scale is equal to 1 unit, determine the least count of the instrument.

• A. $(N+1)$ Main scale division
• B. $(N+1{)}^{-1}$ Main scale divisions
• C. $N$ Main scale division
• D. $(1-N)$ Main scale divsions

Answer 1

Answer: (B)

$(N+1{)}^{-1}$ Main scale divisions

The least count of vernier calipers is $L.C=1MSD-1VSD$ where $MSD=$ main scale division and $VSD=$ vernier scale division.

Given, $N$ $VSD=(N+1)MSD$ or $1VSD=\left[\right(N+1\left)/N\right]$ $MSD$

Thus, $L.C=1MSD-\left[\right(N+1\left)/N\right]MSD=\left[1/\right(N+1\left)\right]MSD=(N+1{)}^{-1}MSD$