$N$ 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
AIEEE 2012, Diffcult
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No of divisions on main scale $=N$
No of divisions on vernier scale $=N+1$
Size of main scale divisions $=a$
Let size of vernier scale division be bthen we have $a N=b(N+1) \Rightarrow b=\frac{a N}{N+1}$
Least count is $a-b=a-\frac{a N}{N+1}$ $=a\left[\frac{N+1-N}{N+1}\right]=\frac{a}{N+1}$
No of divisions on vernier scale $=N+1$
Size of main scale divisions $=a$
Let size of vernier scale division be bthen we have $a N=b(N+1) \Rightarrow b=\frac{a N}{N+1}$
Least count is $a-b=a-\frac{a N}{N+1}$ $=a\left[\frac{N+1-N}{N+1}\right]=\frac{a}{N+1}$
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