Question

One main scale division of a vernier callipers is 'a' cm and n^th division of the vernier scale coincide with (n - 1)^th division of the main scale. The least count of the callipers in mm is ______.

Options

• `(("n"-1)/(10"n"))`a

• `(10"a")/"n"`

• `(10"na")/((n-1)`

• `(10"a")/(("n"-1))`

Answer 1

One main scale division of a vernier callipers is 'a' cm and n^th division of the vernier scale coincides with (n - 1)^th division of the main scale. The least count of the callipers in mm is `bb((10"a")/"n")`.

Explanation:

Given,

1 MSD = a cm

n VSD = (n - 1)MSD

1 VSD = `(("n" - 1))/"n"`MSD

Since, 

LC = 1 MSD - 1 VSD

= 1 MSD - `(("n" - 1))/"n"` MSD ⇒ `"MSD"/"n"`

LC = `"a"/"n"`cm

= `(10"a")/"n"`mm.