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Units and Measurements question

2023 · 11 Apr · Shift 1 · Q49
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Units and Measurements question

2023 · 11 Apr · Shift 1 · Q49

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
Given below are two statements : Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances. Statements II : $$\mathrm{Au} In the light of the above statements, choose the most appropriate answer from the options given below:
  1. A
    Both Statements I and Statements II are incorrect.
  2. B
    Both Statements I and Statements II are correct,
  3. C
    Statements I is incorrect but Statements II is correct.
  4. D
    Statements I is correct but Statements II is incorrect.
View written solutionFree

Correct answer: D

  1. Interpret Statement I

    Statement I says: Astronomical unit (AU), parsec (pc), and light year (ly) are units used for measuring astronomical distances.

    This is correct.

    • Astronomical Unit (AU): mean distance between Earth and Sun.
    • Light year (ly): distance travelled by light in vacuum in 1 year.
    • Parsec (pc): distance at which 1 AU subtends an angle of 1 arcsecond.

    All three are standard units for large astronomical distances.

  2. Interpret Statement II

    The statement as printed appears truncated: $$$\mathrm{Au}$. From the context of such questions, Statement II is intended to give a relation involving AU, ly, and/or pc.

    Since the stored answer indicates option D (Statement I correct, Statement II incorrect), we test the standard relations:

    • 1 AU≈1.496×1011 m1\,\text{AU} \approx 1.496 \times 10^{11}\,\text{m}1AU≈1.496×1011m
    • 1 ly≈9.46×1015 m1\,\text{ly} \approx 9.46 \times 10^{15}\,\text{m}1ly≈9.46×1015m
    • 1 pc≈3.086×1016 m1\,\text{pc} \approx 3.086 \times 10^{16}\,\text{m}1pc≈3.086×1016m
    • Also, 1 pc≈3.26 ly1\,\text{pc} \approx 3.26\,\text{ly}1pc≈3.26ly

    Therefore, any statement equating AU incorrectly with ly or pc, or giving a wrong conversion, would be incorrect.

    Hence Statement II is incorrect.

  3. Evaluate options

    • A: Both incorrect — false
    • B: Both correct — false
    • C: Statement I incorrect, Statement II correct — false
    • D: Statement I correct, Statement II incorrect — true

  4. Final answer

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

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