When a screw gauge of least count 0.01 mm is used to measure the diameter of a wire, the reading on the sleeve is found to be 1 mm and the reading on the thimble is found to be 27 divisions. (1) What is the diameter of the wire in cm? (2) If the zero error is +0.005 cm, what is the correct diameter?

(i) Diameter of the wire = main scale reading + circular scale reading     [Eq 1]

and

Reading on thimble = p x L.C.     [Eq 2]

Given,

p = 27

L.C. = 0.01 mm = 0.001 cm

Substituting the values in Equation 2 we get,

reading on thimble = 27 x 0.001 = 0.027 cm

Hence, reading on thimble = 0.027 cm and reading on sleeve = 1 mm = 0.1 cm

Using Equation 1 we get,

Diameter of the wire = 0.1 cm + 0.027 cm = 0.127 cm

Hence, the diameter of the wire is 0.127 cm.

(ii) Correct reading = observed reading – zero error

Given,

Zero error = + 0.005 cm

Substituting the value of zero error in the formula above we get,

Correct reading = 0.127 cm – 0.005 cm = 0.122 cm

Hence, the correct diameter of the wire is 0.122 cm