A spherically symmetric gravitational system of particles has a mass density
where ρ 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 center of the system is represented by
A
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
C
ρ = ρ 0 , r < R
= 0, r > R
Case I: r < R
F C = 
mg 
(g = acceleration due to gravity at surface of sphere)
V = 
r for r < R
Case II: r > R
= 
V = 
So
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