Question

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 the vernier scale. In measuring the diameter of a cylinder by this instrument, the main scale reads 35 divisions and 4th division of vernier scale coincides with a main scale division. Find

(i) Least count and (ii) Radius of a cylinder.

Answer 1

(i) Value of 1 m.s.d = 1 mm = 0.1 cm

20 vernier divisions = 19 m.s.d.

L.C. = Value of 1 m.s.d./number of divisions on the vernier scale

 = 1mm/20

 = (0.1/20) cm

 = 0.005 cm

(ii) Main scale reading = 35 mm = 3.5 cm

Since 4^th 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 = `"Diameter (Total reading)"/ 2`

 = `(3.52/2)` cm

   = 1.76 cm