First slide

Measurement

Question

The $n^{t h}$ division of main scale coincides with ${(n + 1)}^{t h}$ division of vernier scale. Given one main scale division is equal to $' a'$ units. The least count of vernier is

Moderate

A

$\frac{n}{a + 1}$
B

$\frac{a}{n + 1}$
C

$a n$
D

$\frac{a}{n}$

Solution

$L e a s t C o u n t o f v e r n i e r c a l i p e r s = \frac{v a l u e o f 1 M a i n S c a l e D i v i s i o n}{N u m b e r o f V e r n i e r S c a l e D i v i s i o n} = \frac{a}{n + 1} o b t a i n e d a f t e r s u b s t i t u t i n g t h e g i v e n v a l u e s L e a s t c o u n t = M . S . D - V . S . D G i v e n (n + 1) v s d = n m s d L . C = M . S . D - V . S . D = M . S . D - \frac{n M . S . D}{n + 1} = \frac{1 M . S . D}{n + 1} = \frac{a}{n + 1}$

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