The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n - 1) divisions of main scale. The least count of the vernier callipers is,

Question

The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n - 1) divisions of main scale. The least count of the vernier callipers is, (A) (1/(n +1)(n -1))cm (B) (1/n)cm (C) (1/n2)cm (D) (1/n(n + 1))cm

Tardigrade Admin · Accepted Answer

n(VSD) = (n - 1)MSD ⇒ 1 VSD = ((n - 1)/n) MSD Least count = 1 MSD - 1 VSD = [ 1 - ((n -1)/n)] MSD = (1/n) MSD = (1/n) ((1/n)) cm = (1/n2) cm

Q. The main scale of a vernier callipers has $n$ divisions/cm. $n$ divisions of the vernier scale coincide with (n - 1) divisions of main scale. The least count of the vernier callipers is,

$\frac{1}{( n + 1 ) ( n - 1 )} c m$

$\frac{1}{n} c m$

$\frac{1}{n ^{2}} c m$

$\frac{1}{n ( n + 1 )} c m$

$n (V S D) = (n - 1) MS D$
$\Rightarrow 1 V S D = \frac{( n - 1 )}{n} MS D$
Least count $= 1 MS D - 1 V S D = [1 - \frac{( n - 1 )}{n}]$
$MS D = \frac{1}{n} MS D$
$= \frac{1}{n} (\frac{1}{n}) c m$
$= \frac{1}{n ^{2}} c m$

Q. The main scale of a vernier callipers has n divisions/cm. n divisions of the vernier scale coincide with (n - 1) divisions of main scale. The least count of the vernier callipers is,

(n+1)(n−1)1​cm

n1​cm

n21​cm

n(n+1)1​cm