The Schwarzschild radius of a black hole is that radial distance from the center of a sphere within which not even light can escape. It was first discovered mathematically by Schwarzschild in 1916 after Einstein published his general relativity theory. It can be calculated from a star's mass M as: R = 2GM/c². Take the radius of both stars A and B as the Schwarzschild radius. If the mass of star A is twice as much as the mass of star B, the average density of star A, compared to star B will be A)the same. B)twice as much. C)half as much. D)four times as much. E)one-fourth as much.

Question

Quizplus · Accepted Answer

The Schwarzschild radius is proportional to the mass, so if star A has twice the mass of star B, its radius is also twice as large. Since volume scales with the cube of the radius, the volume of star A is 2^3 = 8 times that of star B. Therefore, the density, which is mass divided by volume, is 1/4 that of star B.

The Schwarzschild Radius of a Black Hole Is That Radial