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Units and Measurements question

2025 · Shift 1 · Q38
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Units and Measurements question

2025 · Shift 1 · Q38

JEE AdvancedPhysicsUnits and MeasurementsMultiple correct+4 / −2
Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm, 0.05 mm, and 6.0 μm, respectively. Which of the following option(s) give(s) the volume of the strip in cm3 with correct significant figures:
  1. A
    3.2×10−53.2 \times 10^{-5}3.2×10−5
  2. B
    32.0×10−632.0 \times 10^{-6}32.0×10−6
  3. C
    3.0×10−53.0 \times 10^{-5}3.0×10−5
  4. D
    3×10−53 \times 10^{-5}3×10−5
View written solutionFree

Correct answer: D

  1. Given measurements

    • Length: 10.5 cm10.5\,\text{cm}10.5cm
    • Breadth: 0.05 mm0.05\,\text{mm}0.05mm
    • Thickness: 6.0 μm6.0\,\mu\text{m}6.0μm

    We need the volume in cm3\text{cm}^3cm3 with correct significant figures.

  2. Convert all quantities to cm

    Breadth

    0.05 mm=0.05×0.1 cm=0.005 cm0.05\,\text{mm} = 0.05 \times 0.1\,\text{cm} = 0.005\,\text{cm}0.05mm=0.05×0.1cm=0.005cm

    Thickness

    Since 1 μm=10−4 cm1\,\mu\text{m} = 10^{-4}\,\text{cm}1μm=10−4cm therefore, 6.0 μm=6.0×10−4 cm6.0\,\mu\text{m} = 6.0 \times 10^{-4}\,\text{cm}6.0μm=6.0×10−4cm

  3. Calculate volume

    V=l×b×tV = l \times b \times tV=l×b×t V=10.5×0.005×6.0×10−4V = 10.5 \times 0.005 \times 6.0 \times 10^{-4}V=10.5×0.005×6.0×10−4

    First, 10.5×0.005=0.052510.5 \times 0.005 = 0.052510.5×0.005=0.0525

    Then, 0.0525×6.0×10−4=0.315×10−4=3.15×10−5 cm30.0525 \times 6.0 \times 10^{-4} = 0.315 \times 10^{-4} = 3.15 \times 10^{-5}\,\text{cm}^30.0525×6.0×10−4=0.315×10−4=3.15×10−5cm3

  4. Determine significant figures

    • 10.510.510.5 has 3 significant figures
    • 0.050.050.05 has 1 significant figure
    • 6.06.06.0 has 2 significant figures

    In multiplication, the result must have the same number of significant figures as the factor with the least number of significant figures.

    So final answer should have 1 significant figure.

    3.15×10−5≈3×10−5 cm33.15 \times 10^{-5} \approx 3 \times 10^{-5}\,\text{cm}^33.15×10−5≈3×10−5cm3

  5. Check options

    • A: 3.2×10−53.2 \times 10^{-5}3.2×10−5 → 2 significant figures, not correct
    • B: 32.0×10−6=3.20×10−532.0 \times 10^{-6} = 3.20 \times 10^{-5}32.0×10−6=3.20×10−5 → 3 significant figures, not correct
    • C: 3.0×10−53.0 \times 10^{-5}3.0×10−5 → 2 significant figures, not correct
    • D: 3×10−53 \times 10^{-5}3×10−5 → 1 significant figure, correct

  6. Conclusion

    The correct option is: D\boxed{D}D​

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