Black Hole Density

Classical Mechanics Level 2

Consider the volume of a black hole to be the volume of a sphere with radius equal to the Schwarzschild radius R S = 2 G M c 2 R_{S} = \frac{2 G M}{c^{2}} .

How does the average density of a black hole change as the mass increases?

Stays the same Decreases Increases

Adam Strandberg by Adam Strandberg , 28, USA

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3 solutions

Adam Strandberg
Feb 10, 2016

Since the radius is proportional to M M , the volume is proportional to M 3 M^{3} . The average density, D = M V D = \frac{M}{V} is therefore proportional to 1 M 2 \frac{1}{M^{2}} , which decreases as M M increases.

21 Helpful 13 Interesting 9 Brilliant 3 Confused

density is directly proportional to the mass so as mass increase density also increase

umakshi sharma - 2 years, 2 months ago

https://www.youtube.com/watch?v=brmjWYQi2UM this might help top understand this

Masskito Typ - 1 year, 8 months ago

Got mine correct

Kay Vincent - 1 year, 6 months ago
Anson Odeny
Jan 25, 2021

For example if the mass M increases twice,the radius becomes 2R, the new volume becomes 8V, after substituting R³ with the new (2R)³. The new density becomes the newM/newV = 2M/8V = M/4V hence the density decreases

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Remember, volume is not the same as mass,

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