Sun April 19, 2015 By: Smriti Rani

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

Expert Reply
Jyothi Nair
Mon April 20, 2015

Given that:

Value of 1 m.s.d = 1 mm = 0.1 cm

20 vernier divisions = 19 main scale divisions


begin mathsize 12px style Least space Count space equals fraction numerator Value space of space 1 space straight m. straight s. straight d over denominator Number space of space divisions space on space the space vernier space scale end fraction equals fraction numerator 1 space mm over denominator 20 space cm end fraction equals fraction numerator 0.1 over denominator 20 end fraction cm equals 0.005 space cm end style

Least count = 0.005 cm


Given that:

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

begin mathsize 12px style Radius space of space the space cylinder equals fraction numerator Total space reading space left parenthesis Diameter space reading right parenthesis over denominator 2 end fraction space equals space fraction numerator 3.52 over denominator 2 end fraction cm space equals 1.76 space cm end style

 = (3.52/2) cm

   = 1.76 cm

Radius of the cylinder = 1.76 cm

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