The diameter of a thin wire is measured by using a screw gauge having 100 divisions on circular scale. When spindle of screw gauge is touched to anvil, then zero of circular scale lies 6 division above the reference line of main scale. Now, when wire is kept between spindle and anvil then 30^thdivision of circular scale exactly coincides with the reference line of main scale as shown in the figure. The distance between two successive divisions of main scale is 0.1 mm. The measured diameter of wire is found to be $5 . XYZ mm$ ,where X,Y and Z are non negative single digit integers. Find the value of $X+Y+Z$ (pitch of the screw gauge is 0.1mm)

Question

The diameter of a thin wire is measured by using a screw gauge having 100 divisions on circular scale. When spindle of screw gauge is touched to anvil, then zero of circular scale lies 6 division above the reference line of main scale. Now, when wire is kept between spindle and anvil then 30^thdivision of circular scale exactly coincides with the reference line of main scale as shown in the figure. The distance between two successive divisions of main scale is 0.1 mm. The measured diameter of wire is found to be $5 . XYZ mm$ ,where X,Y and Z are non negative single digit integers. Find the value of $X+Y+Z$ (pitch of the screw gauge is 0.1mm)

Infinity Learn · Accepted Answer

Pitch = 0.1mm, N = 100Least count =0.1100=0.001mmNegative zero error =6×0.001=0.006mmReading of screw gauge =(50×0.1)mm+(30×0.001)mm=5.03mmMeasured value =(5.03+0.006)mm=5.036mm

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