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  4. A screw gauge with a pitch of 1 mm has 100 divisions on its circular scale. When it is used to measure the diameter of a thin wire, the main scale reading is 3 mm and the circular scale reading is 45. If D is the diameter of the wire in m m, then find the value of D.

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Q. A screw gauge with a pitch of $1 \, mm$ has $100$ divisions on its circular scale. When it is used to measure the diameter of a thin wire, the main scale reading is $3 \, mm$ and the circular scale reading is $45.$ If $D$ is the diameter of the wire in m $m,$ then find the value of $D.$

NTA AbhyasNTA Abhyas 2020Physical World, Units and Measurements

Solution:

$Least \, count \, =\frac{P i t c h}{N o . \, o f \, d i v i s i o n}=\frac{1 m m}{100}=0.01 \, mm$
$Diameter \, of \, wire \, = \, main \, scale \, + \, circular \, scale \, reading$
$=3 \, mm+\left(L . C\right)\times No. \, of \, division$
$=3 \, mm+0.01\times 45$
$D=3.45 \, mm$