Chapter 34, Problem 23PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

# Black holes with masses smaller than muse formed in supernovas may have been created in the Big Bang. Calculate the radius of one that has a mass equal to the Earthâ€™s.

To determine

The Schwarzschild radius of a black hole having a mass equal to mass of the earth.

Explanation

Given:

Mass of Earth, me=5.972Ă—1024â€‰kg

Speed of light, c=3Ă—108â€‰m/s

Gravitational constant, G=6.67Ă—10âˆ’11â€‰N-m2/kg2

Formula used:

Formula to calculate the Schwarzschild radius of a black hole is,

â€ƒâ€ƒRsc=2Gmc2 ...... (I)

Where,

• Rsc is Schwarzschild radius of black hole.
• G is gravitational constant.
• m is mass of the black hole.
• c is speed of light.

Calculation:

Since, the mass of the black is equal to the mass of the earth.

Calculate the mass of the black hole.

â€ƒâ€ƒm=me

Substitute 5.972Ă—1024â€‰kg for me in the above expression.

â€ƒâ€ƒm=5.972Ă—1024â€‰kg

Substitute 5.972Ă—1024â€‰kg for m , 6

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