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 coincides with a main scale division. Find — (i) least count and (ii) radius of cylinder.

(i) Value of one main scale division(x) = 1 mm

Total number of divisions on vernier callipers (n) = 20

Substituting the values in the formula above we get,

L.C. = 1/20

$\text{L.C.}=0.05\text{mm}$

$\text{L.C.}=0.005\text{cm}$

Hence, the least count of the vernier callipers is 0.005 cm.

(ii) Circular scale reading = L.C. × Coinciding division

Coinciding division = 4

L.C. = 0.005 cm

Substituting the values in the formula above we get,

circular scale reading=0.005 cm × 4

⇒ circular scale reading = 0.02 cm

Hence, the circular scale reading = 0.02 cm. …… (1)

Main scale reading = 3.5 cm (as it reads 35th division on mm scale)

Hence, the main scale reading = 3.5 cm. …….. (2)

Substituting the values 1 and 2 in the formula for total reading we get,

Total reading = main scale reading + vernier scale reading

Diameter = Total reading

= 3.5 cm + 0.02 cm

⇒ Diameter = 3.5/2 cm

⇒ Radius=1.76cm

Hence, the radius of the cylinder = 1.76 cm.