One main scale division of a vernier callipers is ' $a$ ' cm and $n^{ ext {th }}$ division of the v

Question

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

Professor PC Thomas Classes · Answer

(c) : One main scale division, 1 M.S.D. $=a \mathrm{~cm}$
$n^{	ext {th }}$ division of the vernier scale division are equal to $(n-1)^{	ext {th }}$ division of main scale, We get
1 V.S.D. $=\frac{(n-1)^{	ext {th }}}{n^{	ext {th }}} \mathrm{mm}$
The least count is given by
$=1$ MSD -1 VSD
$=\left(a-\frac{(n-1)}{(n)} 	imes aight) \mathrm{cm}=\frac{n a-(n-1) a}{n} \mathrm{~cm}$