The mass density of a spherical galaxy varies as over a large distance from its centre

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

Problem

The mass density of a spherical galaxy varies as

\frac{K}{r}

over a large distance

r

from its centre. In that region, a small star is in a circular orbit of radius

R

. Then the period of revolution,

T

depends on

R

as : (1)

T^2 \propto R

(2)

T^2 \propto R^3

(3)

T^2 \propto \frac{1}{R^3}

(4)

T \propto R