Question

The main scale, of a given screw gauge, has been graduated in ‘half millimeters’.

The moving jaw of this screw gauge advances through 2.5 mm, on the main scale, when the screw is given five complete rotations. There are 100 divisions on its circular scale. 

The zero of the circular scale, coincides with the zero of the main scale when the moving face end just coincides with its fixed face end. 

When a thin sheet is just held between the jaws of the screw guage, the main scale reads 0.55 cm while the 43^rd division, of the circular scale, lies along the line of graduations of the main scale. The least count of this screw gauge, and the thickness of the sheet, are equal, respectively, to

(1) 0.0005 mm and 0.5715 cm

(2) 0.0005 cm and 0.55215 cm

(3) 0.0005 mm and 0.55215 cm

(4) 0.0005 cm and 0.5715 cm

Answer 1

(4) 0.0005 cm and 0.5715 cm

The pitch of the screw gauge = 2.5/5 mm = 0.5 mm

∴ Least count = 0.5/100 mm = 0.005 mm = 0.0005 cm

Main scale reading = 0.55 cm 

Circular scale reading = 43 x 0.0005 cm 

= 0.0215 cm 

∴ Thickness of the sheet 

= 0.5715 cm