A vernier callipers has its main scale graduated in mm and 10 divisions on its vernier scale are equal in length to 9 mm. When the two jaws are in contact, the zero of vernier scale is ahead of zero of main scale and 3rd division of vernier scale coincides with a main scale division. Find — (i) the least count and (ii) the zero error of the vernier callipers.

(i) Total number of divisions on vernier (n) = 10

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

Substituting the values in the formula above, we get,

L.C.  = 1/10 mm​

L.C. = 0.1 mm

L.C. = 0.01 cm

Hence, the least count of the vernier callipers is 0.01cm.

(ii) As we know,

Zero error = L.C. × Coinciding division (with sign)

and Coinciding division = 3

L.C. = 0.01 cm

Substituting the values in the formula above we get,

Zero error = 0.01 cm × 3 cm

Zero error = 0.01 cm × 3

⇒ Zero error = 0.03 cm

Hence, the zero error of the vernier callipers = + 0.03 cm.