Circular MotionMedium
Question
A spherically symmetric gravitational system of particles has a mass density ρ = 
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
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
Options
A.
B.
C.
D.
Solution
G
πρ0r = 
, r ≤ R
Hence, v ∝ r
r ≥ R
Hence v ∝
πρ0r = , r ≤ RHence, v ∝ r
r ≥ R Hence v ∝
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