Question

N divisions on the main scale of a vernier calliper coincide with (N + 1) divisions of the vernier scale. If each division of main scale is '$a$' units, then the least count of the instrument is.

• A. $a$
• B. $\frac{a}{N}$
• C. $\frac{N}{N+1}$ $\times a$
• D. $\frac{a}{N+1}$

Answer 1

The correct option is D $\frac{a}{N+1}$

$(n+1)VSD=nMSD$

$1VSD=\frac{n}{n+1}MSD$

least count of vernier callipers

$=1MDS-1VSD$

$=[1-\frac{n}{n+1}]MSD$

$=\left[\frac{a}{n+1}\right]unit.$

Hence (D) is the correct answer.