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

Answer: (D)

No of divisions on main scale $= N$
No of divisions on vernier scale $= N + 1$
size of main scale division $= a$
Let size of vernier scale division be $b$ then we have
$aN=b\left(N+1\right) \Rightarrow b=\frac{aN}{N+1}$
Least count is $a - b =a-\frac{aN}{N+1}$
$=a\left[\frac{N+1-N}{N+1}\right]=\frac{a}{N+1}$