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Question

There exists a spherically symmetric gravitational system of particles of radius R. Its speed V as a function of distance r(0<r<) from the centre of the system is represented by


Your Answer
A
Your Answer
B
Correct Answer
C
Your Answer
D

Solution

The correct option is B

For the first region: 0<r<R
Total force= 43πr3Gmρr2=43πrGmρ

Here, gravitation force is equal to the centripetal force, 
43πrGmρ=mv2rv2r2 or vr


In the second condition: R<r<
F=43πR3Gmρr2 
again,
Gravitational force = centripetal force
43πR3Gmρr2=mv2r 
so, vR3/2v1r1/2
hence, 
So, option C is correct.

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