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KVPY2010PhysicsGravitation

A certain planet completes one rotation about its axis in time T . The weight of an object placed at the equator on the planet's surface is a fraction f (f . is close to unity) of its weight recorded at a latitude of 60^ . The density of the planet (assumed to be a uniform perfect sphere is given by-

Options

  1. A4-f 1-f 3 4 GT ²
  2. B4-f 1+f 3 4 G T²
  3. C4-3 f 1-f 3 4 G T²
  4. D4-2 f 1-f 3 4 GT ²

Correct answer

A. 4-f 1-f 3 4 GT ²

Step-by-step solution

v = GM r also T = 2 r v or T =2 r ³ GM when v is replaced by GM r now g_ e f f =g- ² R_ e ² now f= g- ² R_ e 0^ g- ² R_ e 60^ ving we get R _ e = 4 g( f -1) ²( f -4) or GM R _ e ² ( f -1)= ² R _ e 4 ( f -4) R _ e ³= 4 GM ² ( f -1) ( f -4) now = M 4 3 R_ e ³ = 3 16 ² G (f-4) (f-1) also T = 2 p = 3 ( f -4) 4 ~T ² G ( f -1)

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