A spherically symmetric gravitational system of particles has a mass density = array l ₀ for r R 0 for rR array . where ₀ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. I

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A spherically symmetric gravitational system of particles has a mass density = array l ₀ for r R 0 for r>R array . where ₀ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed v as a function of distance r(0 < r < ) from the centre of the system is represented by

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Correct answer: 2

For r R : m v^2 r = G m m^ r^2 Here, m^ = ( 4 3 r^3 ) ₀ Substituting in Eq. (i) we get, v r i.e., v-r graph is a straight line passing through origin. For r>R : m v^2 r = G m ( 4 3 R^3 ) ₀ r^2 or V 1 r The corresponding v-r graph will be as shown in option (c). correct option is (c).

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