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JEE Main
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Physics
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Experimental Physics

JEE Main · Physics · Experimental Physics

Two full turns of the circular scale of a screw gauge having 50...

Two full turns of the circular scale of a screw gauge having 5050 divisions cover a distance of 11 mm.~Further, it is found that the screw gauge has a zero error of −0.02mm- 0 . 02mm. While measuring the diameter of a thin wire, a student notes the main scale reading of 44 mm and the number of circular scale divisions in line with the main scale as 3737. The diameter of the wire is,

Options

  1. A4.37mm4 . 37mm
  2. B4.39mm4 . 39mm
  3. C4.74mm4 . 74mm
  4. D4.76mm4 . 76mm

Correct answer

B. 4.39mm4 . 39mm

Step-by-step solution

Distance cover in 11 full turn will be~1mm2=0.5mm\dfrac{1mm}{2} = 0 . 5mm.

Least count of screw gauge,

LC=Distancecoverin1fullturnnumberofdivisionincircularscale=0.5mm50=0.01mmLC = \dfrac{Distancecoverin1fullturn}{numberofdivisionincircularscale} = \dfrac{0 . 5mm}{50} = 0 . 01mm

Reading of the screw gauge,R=mainscalereading+Circularscalereading×LCR = mainscalereading + Circularscalereading \times LC

R=4mm+37×0.01mm=4.37mmR = 4mm + 37 \times 0 . 01mm = 4 . 37mm

Reading without zero error,~R′=R−zeroerror=4.37mm−(−0.02mm)=4.39mmR^{'} = R - zeroerror = 4 . 37mm - \left(- 0 . 02mm\right) = 4 . 39mm

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