In a vernier calipers, one main scale division is x cm and n division of the vernier scale coincide with ( n -1) divisions of the main scale. The least count (in cm ) of the calipers is:

Question

In a vernier calipers, one main scale division is x cm and n division of the vernier scale coincide with ( n -1) divisions of the main scale. The least count (in cm ) of the calipers is: (A) (( n -1/ n )) x (B) (( nx / n -1)) (C) (x/n) (D) ((x/n-1))

Tardigrade Admin · Accepted Answer

One main scale division, 1 M.S.D = x cm One vernier scale division, 2 V.S.D =(( n -1) x / n ) Least count =1 M.S.D -1 V.S.D =(nx-nx+x/n)=(x/n) cm

Q. In a vernier calipers, one main scale division is $x c m$ and $n$ division of the vernier scale coincide with $(n - 1)$ divisions of the main scale. The least count (in $c m$ ) of the calipers is:

$(\frac{n - 1}{n}) x$

$(\frac{n x}{n - 1})$

$\frac{x}{n}$

$(\frac{x}{n - 1})$

One main scale division, $1 M . S . D = x c m$
One vernier scale division, $2 V . S . D = \frac{( n - 1 ) x}{n}$
Least count $= 1 M . S . D - 1 V . S . D$
$= \frac{n x - n x + x}{n} = \frac{x}{n} c m$

Q. In a vernier calipers, one main scale division is xcm and n division of the vernier scale coincide with (n−1) divisions of the main scale. The least count (in cm ) of the calipers is:

(nn−1​)x

(n−1nx​)

nx​

(n−1x​)