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JEE Main2015PhysicsGravitationActual

A very long (length L ) cylindrical galaxy is made of uniformly distributed mass and has radius R ( R < < L ) . A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of the star is T and its distance from the galaxy's axis is r , then

Options

  1. AT ∝ r
  2. BT ∝ r
  3. CT ∝ r 2
  4. DT 2 ∝ r 3

Correct answer

B. T ∝ r

Step-by-step solution

Due to a long solid cylinder gravitational field strength can be given as, g =   2   G   λ r Where, λ = linear mass density of galaxy.   For the orbital motion around the galaxy, f g = f c e n t r i p e t a l ⇒               m g = m   ω 2 r   ⇒               2 G λ r = ω 2 r ⇒             ω 2   ∝ 1 r 2 ⇒      

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