The main scale of vernier calipers is calibrated in mm and 19 divisions of the main scale are equal in length to 20 divisions of the vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and the 4th division of the vernier scale coincides with the main scale division. Find :
(i) least count
(ii) radius of the cylinder.

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Solution

(i)
Given,
Value of 1 m.s.d = 1 mm = 0.1 cm
20 vernier divisions = 19 m.s.d.
We know,
$L C = \frac{V a l u e o f o n e m s d}{N u m b e r o f d i v i s i o n s o n s c a l e}$
Putting all the values
$L C = \frac{0.1}{20} = 0.005$
Hence the least count is 0.005.

(ii)
Main scale reading = 35 mm = 3.5 cm
Since 4th division of the main scale coincides with the main scale, i.e. p = 4.
Therefore, the vernier scale reading = 4 × 0.005 cm = 0.02 cm
Total reading = Main scale reading + vernier scale reading
= (3.5 + 0.02) cm
= 3.52 cm
Radius of the cylinder = $\frac{D i a m e t e r (T o t a l r e a d i n g)}{2}$
Or, $R a d i u s = \frac{3.52}{2} = 1.76$
Hence the radius is 1.76 cm.

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