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Q.

A spherically symmetric gravitational system of particles has a mass density ρ=ρ0     for r≤R0     for r>R Where ρ0 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed v as function of distance r from the centre of the system is represented by

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a

b

c

d

answer is C.

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Detailed Solution

For r≤R;mv2r=GmMr2→(1)here, M=43πr3ρ0substituting in Eq(1) we get v ∞ ri.e., v-r graph is a straight line passing through origin. for r > Rmv2r=Gm34πR3ρ0r2 or v∞1rThe corresponding v-r graph will be as shown in option (3)
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