Question

Use equation 2.18 to find the mass m(< r₀) within a sphere of radius r₀ about the galactic center.

a. m(r₀) = (4/3)πr₀³rho₀
b. m(r₀) = 4πr₀²σ
c. m(r₀) = (1/2)πr₀²μ
d. m(r₀) = (1/3)πr₀³λ

Answer 1

The mass within a sphere of radius r0 around the galactic center is given by the equation m(r0) = (4/3)πr0³ρ0, which takes into account the symmetrical mass distribution and uses the density multiplied by the sphere's volume. Hence, the correct option is (a).

Step-by-step explanation:

To find the mass m(< r0) within a sphere of radius r0 about the galactic center, we consider that for any spherical body, the mass can be assumed to be concentrated at its center. This implies that when dealing with symmetrical mass distributions, we can use the formula for the volume of a sphere multiplied by its density to find the mass within a given radius.

The correct equation to use, taking into account the context provided, would be:

m(r0) = (4/3)πr0³ρ0, where ρ0 stands for the density at the center or average density of the sphere.