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JEE Main 2015 Physics question

PhysicsGravitationJEE Main 2015

A very long (length ) cylindrical galaxy is made of uniformly distributed mass and has radius . 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 and its distance from the galaxy's axis is , then

Answer: (2)

Solution

For an infinitely long uniform cylinder, Gauss's law for gravity applied to a coaxial cylinder of radius and length gives , so , where is the mass per unit length. The gravitational field therefore falls off as , not

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Question ID VK-115230