The Schwarzchild 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 Schwarzchild in 1916 after Einstein published his general relativity theory. It can be calculated from a star's mass M as: R = 2GM/c². If the mass of star G is twice as much as the mass of star H, the average density of star G compared to star H will be A) twice as much. B) four times as much. C) half as much. D) one-fourth as much.

Question

Quizplus · Accepted Answer

The Schwarzchild radius (R) is directly proportional to the mass (M) of the object, as shown in the formula R = 2GM/c^2. If the mass of star G is twice that of star H, the radius of star G's Schwarzchild sphere will also be twice that of star H, assuming they collapse into black holes. Since volume (V) is proportional to the cube of the radius (V ∝ R^3), the volume of star G's Schwarzchild sphere will be 2^3 = 8 times that of star H. Therefore, if the mass is doubled but the volume increases by a factor of 8, the average density (mass/volume) of star G will be one-fourth that of star H.

The Schwarzchild Radius of a Black Hole Is That Radial