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1. units,dimensions and measurement — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics1. units,dimensions and measurement1 Mark
MCQ
Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 mm$. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.

Measurement condition Main scale reading Circular scale reading
Two arms of gauge touching each other without wire $0$  division $4$ division
Attempt-$1$: With wire $4$  division $20$ division 
Attempt-$2$: With wire $4$ division $16$ division

What are the diameter and cross-sectional area of the wire measured using the screw gauge?

  • A
    $2.22 \pm 0.02 mm , \pi(1.23 \pm 0.02) mm ^2$
  • B
    $2.22 \pm 0.01 mm , \pi(1.23 \pm 0.01) mm ^2$
  • ✓
    $2.14 \pm 0.02 mm , \pi(1.14 \pm 0.02) mm ^2$
  • D
    $2.14 \pm 0.01 mm , \pi(1.14 \pm 0.01) mm ^2$
✓

Answer

Correct option: C.
$2.14 \pm 0.02 mm , \pi(1.14 \pm 0.02) mm ^2$
c
$\text { LC }=\frac{0.1}{100}=0.001 mm$

$\text { Zero error }=4 \times 0.001=0.004 mm$

$\text { Reading } 1=0.5 \times 4+20 \times 0.001-0.004=2.16 mm$

$\text { Reading } 2=0.5 \times 4+16 \times 0.001-0.004=2.12 mm$

$\text { Mean value }=2.14 mm$

$\text { Mean absolute error }=\frac{0.02+0.02}{2}=0.02$

$\text { Diameter }=2.14 \pm 0.02$

$\text { Area }=\frac{\pi}{4} d^2$

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