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Question

# 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 a function of distance r(0<r<∞) from the centre of the system is represented by

A
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B
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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 V∝r Using the equation for centripetal force on test mass for a point outside the sphere for r≥R⇒GMr2=mV2r ⇒V2∝1r

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