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Young's Modulus of Elasticity

A vernier cal...

Question

A vernier callipers has its main scale graduated in mm and 10 divisions on its vernier scale are equal in length to 9 mm. When the two jaws are in contact. the zero of vernier scale is ahead of zero of main scale and 3rd division of vernier scale coincides with a main scale division. The least count is $10^{- x} c m$ . Find the value of x.

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Solution

Value of one main scale division is $1 m m$
$10$ div of vernier scale $= 9 m m$ .
$1$ div of vernier scale $= 9 / 10 m m$ .
Least count $= L . C . =$ Value of one main scale division $-$ Value of one vernier scale division
$L . C =$ $1 - \frac{9}{10} = 1 m m - 0.9 m m = 0.1 m m = 0.01 c m$

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