Consider a spherical gaseous cloud of mass density in a free space where is the…

PHYSICS · Single correct · AP · Physics C: Mechanics · Force and Translational Dynamics · Force and Translational Dynamics

Problem

Consider a spherical gaseous cloud of mass density

\rho(r)

in a free space where

r

is the radial distance from its center. The gaseous cloud is made of particles of equal mass

m

moving in circular orbits about the common centre with the same kinetic energy

K

. The force acting on the particles is their mutual gravitational force. If

\rho(r)

is constant in time. The particle number density

n(r) = \rho(r)/m

is [G is universal gravitational constant] [Adv. 2019] (1)

\frac{3K}{\pi r^2 m^2 G}

(2)

\frac{K}{2\pi r^2 m^2 G}

(3)

\frac{K}{\pi r^2 m^2 G}

(4)

\frac{K}{6\pi r^2 m^2 G}