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Certain spherical astronomical objects radiate as black bodies and have surface temperature inversely proportional to their radii. Object X has twice the radius of object Y. The power radiated by X divided by that radiated byY is (A) 0.25 (B) 0.4 (C) 0.125 (D) 8 Answer is A explain?
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Certain spherical astronomical objects radiate as black bodies and hav...
Explanation:

  • Let the radii of objects X and Y be rX and rY respectively.

  • Let the surface temperature of object X be TX and that of object Y be TY.

  • According to the given condition, TX ∝ 1/rX and TY ∝ 1/rY.

  • Let the power radiated by objects X and Y be PX and PY respectively.

  • According to Stefan-Boltzmann's law, P = σAeT4, where σ is the Stefan-Boltzmann constant, A is the surface area of the object and e is its emissivity.

  • Since both objects radiate as black bodies, their emissivity is equal to 1.

  • Therefore, PX = σ4πrX2TX4 and PY = σ4πrY2TY4.

  • Dividing PX by PY, we get:

    PX/PY = σ4πrX2TX4 / σ4πrY2TY4

    PX/PY = (rX/rY)2 (TX/TY)4

    PX/PY = (rX/rY)2 (rY/rX)4

    PX/PY = (rX/rY)-2 (rX/rY)4

    PX/PY = (rX/rY)2 = (2/1)2 = 4.

  • Therefore, the answer is (A) 0.25, as PY/PX = 1/4.
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Certain spherical astronomical objects radiate as black bodies and hav...
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Certain spherical astronomical objects radiate as black bodies and have surface temperature inversely proportional to their radii. Object X has twice the radius of object Y. The power radiated by X divided by that radiated byY is (A) 0.25 (B) 0.4 (C) 0.125 (D) 8 Answer is A explain?
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Certain spherical astronomical objects radiate as black bodies and have surface temperature inversely proportional to their radii. Object X has twice the radius of object Y. The power radiated by X divided by that radiated byY is (A) 0.25 (B) 0.4 (C) 0.125 (D) 8 Answer is A explain? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Certain spherical astronomical objects radiate as black bodies and have surface temperature inversely proportional to their radii. Object X has twice the radius of object Y. The power radiated by X divided by that radiated byY is (A) 0.25 (B) 0.4 (C) 0.125 (D) 8 Answer is A explain? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Certain spherical astronomical objects radiate as black bodies and have surface temperature inversely proportional to their radii. Object X has twice the radius of object Y. The power radiated by X divided by that radiated byY is (A) 0.25 (B) 0.4 (C) 0.125 (D) 8 Answer is A explain?.
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