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AP EAMCET2003PhysicsThermal Properties of Matter

The radiation emitted by a star A is 10000 times that of the sun. If the surface temperatures of the sun and the star A are 6000 ~K and 2000 ~K respectively, the ratio of the radii of the star A and the sun is :

Options

  1. A300: 1
  2. B600: 1
  3. C900: 1
  4. D1200: 1

Correct answer

C. 900: 1

Step-by-step solution

Energy radiated per unit time E= A T^4 where = Stefan's constant For sun E_ sun = A_ sun T_ sun ^4 According to question, E_ star =10000 E_ sun A_ star T_ star ^4=10000 A_ sun T_ sun ^4 R_ star ^2 T_ star ^4=10000 R_n^2 T_ sun ^4 ( R_ star R_ sun )^2=10000 ( T_ sun T_ star )^4=10000 ( 6000 2000 )^4 R_ star R_ sun = 10000 (3)^4 =100 3^2=900R_ star : R_ sun =900: 1

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