A meter scale is truly calibrated at 20°C whose least count is 1 mm. If the coefficient of linear expansion of scale is l.2 x l0^–5C^–1 then what will be the least count at temperature 120°C and actual length of bar, if measured length of this bar is 40cm?

Solution

Least count of scale is 1 mm, which means that the value of 1 division of calibration is 1 mm.

The distance between the divisions will increase, when the rod is heated to temperature 120°.
At 120°C the length of 1 division becomes,

straight y space equals straight x left parenthesis 1 plus αθ right parenthesis space space space equals space 1 left parenthesis 1 plus 1.2 cross times 10 to the power of negative 5 end exponent cross times 100 right parenthesis space mm space space space equals space 1 plus 0.0012 space equals space 1.0012 space mm

Thus least count of scale at 120°C increases to 1.0012 mm.
Measured length of rod with hot scale is,

space space space straight L subscript straight m equals 40 space cm space space space space space space space space equals space 400 space div.

Least count of hot scale = 1.0012 mm
Therefore actual length of rod is,

straight L subscript straight a equals 400 cross times 1.0012 mm space space space space space equals space 400.48 mm space space space space space equals space 40.048 space cm

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