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Question
Black holes with masses smaller than those formed in supernovas may have been created in the Big Bang. Calculate the radius of one that has a mass equal to the Earth's.
Question by OpenStax is licensed under CC BY 4.0.
Final Answer
$8.86 \textrm{ mm}$
No wonder they are so hard to observe!
Solution Video

OpenStax College Physics Solution, Chapter 34, Problem 23 (Problems & Exercises) (0:36)

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Video Transcript

This is College Physics Answers with Shaun Dychko. We are going to calculate the size of a black hole that has the mass of the Earth. So the Schwarzschild radius from equation 2 in chapter 34 it's 2 times the gravitational constant times the mass divided by <i>c</i> squared. So this is the distance to the event horizon around the black hole and so that's gonna be 2 times 6.67 times 10 to the minus 11 newton meter squared per kilogram squared times mass of the Earth divided by the speed of light squared giving a radius of 8.86 millimeters.

Solutions for problems in chapter 34