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 [2019]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

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 [2019]

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

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

3 $\frac{1}{n^{2}} c m$

4 $\frac{1}{n (n + 1)} c m$

Ans.
(3)

If n divisions of the vernier scale coincide with (n−1) divisions of the main scale:

Therefore, $n V S D = (n - 1) M S D \Rightarrow 1 V S D = \frac{(n - 1)}{n} M S D$

Least count= $1 M S D - 1 V S D = 1 M S D - \frac{(n - 1)}{n} M S D = 1 M S D - 1 M S D + \frac{1}{n} M S D = \frac{1}{n} M S D$
= $\frac{1}{n} \times \frac{1}{n} = \frac{1}{n^{2}} c m$ $⋮ [1 M S D = \frac{1}{n} c m]$

Want Us to Email you About Special Offers & Updates?