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Question

A spherically symmetric gravitational system of particles has a mass density ρ={ρ0 for rR0 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 a function of distance r(0<r<) from the centre of the system is represented by

A
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C
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D
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Solution

The correct option is C


Using the equation for centripetal force on test mass for a point inside the sphere
For r<R
GMrR3=mV2r
Vr
Using the equation for centripetal force on test mass for a point outside the sphere
for rRGMr2=mV2r
V21r

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