A screw gauge has some zero error but its value is unknown. We have two identical rods. When the first rod is inserted in the screw, the state of the instrument is shown by diagram ( ). When both the rods are inserted together in series then the state is shown by the diagram ( ). What is the zero error of the instrument?
Note : 1 msd = 100 csd = 1 mm
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Least count of screw gauge = 0 . 0 1 m m
Reading is noted as
Main scale reading+(circular scale reading)*least count
let us take z e r o e r r o r to be positive and be x
Actual reading =Observed reading -zero error
reading from diagram 1
2 + ( 1 2 − x ) × 1 0 − 2 m m .............................. ( 1 )
reading from diagram 2
4 + ( 1 0 − x ) × 1 0 − 2 m m ................................. ( 2 )
As the rods are identical so reading of two rods must be equal
2 × ( 1 ) = ( 2 )
2 ( 1 2 − x ) = ( 1 0 − x )
x = 1 4
since x comes out to be positive so our assumption of taking zero error positive is correct,
so zero error x = + 0 . 1 4 m m