A microscope is provided with a main scale graduated with 20 divisions in 1 cm and a vernier scale with 25 divisions on it coinciding with 24 divisions of main scale. The least count of the microscope is $2 \times 10^{- x} c m$ . Find the value of x.

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Solution

$25 \times$ Vernier scale reading (vsd) $= 24 \times$ main scale reading (msd)
$1 v s d = 0.96 m s d$
Least count $= 1 m s d - 1 v s d$
$= 0.04 m s d$
$1 m s d = \frac{1}{20} c m$
Least count $= \frac{1}{20} \times 0.04 = 0.002 c m$

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A microscope is provided with a main scale graduated with 20 divisions in 1 cm and a vernier scale with 25 divisions on it coinciding with 24 divisions of main scale. The least count of the microscope is 2×10−xcm. Find the value of x.

25 × Vernier scale reading (vsd) =24 × main scale reading (msd)1 vsd=0.96 msdLeast count =1 msd−1 vsd =0.04 msd1 msd=120cm Least count =120×0.04=0.002 cm

A microscope is provided with a main scale graduated with 20 divisions in 1 cm and a vernier scale with 25 divisions on it coinciding with 24 divisions of main scale. The least count of the microscope is $2 \times 10^{- x} c m$ . Find the value of x.

$25 \times$ Vernier scale reading (vsd) $= 24 \times$ main scale reading (msd)
$1 v s d = 0.96 m s d$
Least count $= 1 m s d - 1 v s d$
$= 0.04 m s d$
$1 m s d = \frac{1}{20} c m$
Least count $= \frac{1}{20} \times 0.04 = 0.002 c m$