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

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) (a/N) (C) (N/N+1)× a (D) (a/N+1)

Tardigrade Admin · Accepted Answer

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(N+1) ⇒ b=(aN/N+1) Least count is a - b =a-(aN/N+1) =a[(N+1-N/N+1)]=(a/N+1)

Q. $N$ 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

$a$

$\frac{a}{N}$

$\frac{N}{N + 1} \times a$

$\frac{a}{N + 1}$

Q. 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

Na​

N+1N​×a

N+1a​

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(N+1)⇒b=N+1aN​ Least count is a−b=a−N+1aN​ =a[N+1N+1−N​]=N+1a​

Q. $N$ 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

$a$

$\frac{a}{N}$

$\frac{N}{N + 1} \times a$

$\frac{a}{N + 1}$