Student A and Student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolute value of the difference between the final circular scale readings observed by the students A and B is ____. [Figure shows position of reference 'O' when jaws of screw gauge are closed] Given pitch =0.1cm.
Answer: 13
Solution
The least count is divisionspitch=1000.1=0.001 cm. With the jaws closed the reference line of the first gauge stands at the circular division 5, a zero error of +5 divisions, while on the second it stands at 92, which is 8 divisions short of a full turn and so a zero error of −8 divisions. Each observed reading is the true value shifted by that gauge's zero error, so the two students read
0.322+0.005=0.327cm,0.322−0.008=0.314cm
The main scale supplies 0.300 cm in both cases, leaving circular scale readings of 27 and 14. The difference between the two circular scale readings is 13.