Chapter 34, Problem 24PE

### 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

# Supermassive black holes are thought to exist at the center of many galaxies.(a) What is the radius of such an object if it has a mass of 109 Suns?(b) What is this radius in light years?

To determine

(a)

The radius of the object having a mass of 109 times the mass of the sun.

Explanation

Given:

Mass of Sun, ms=1.989Ã—1030â€‰kg

Speed of light, c=3Ã—108â€‰m/s

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

Formula used:

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

â€ƒâ€ƒRsc=2Gmc2 ...... (I)

Where,

• G is gravitational constant.
• m is mass of the object.
• c is speed of light.

Calculation:

Super massive black holes are thought to exist at the center of any galaxy and these are the largest type of the black holes. In order to determine the radius of the object, determine the Schwarzschild radius.

Since, the mass of the object is 109 times the mass of the sun.

Calculate the mass of the black hole.

â€ƒâ€ƒm=109Ã—ms

Substitute 1.989Ã—1030â€‰kg for me in the above expression.

â€ƒâ€ƒm=109Ã—1.989Ã—1030â€‰kg=1.989Ã—1039â€‰kg

Substitute 1

To determine

(b)

The radius of the object in terms of light years.

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