Chapter 34, Problem 25PE

### 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

# Construct Your Own ProblemConsider a supermassive black hole near the center of a galaxy. Calculate the radius of such an object based on its mass. You must consider how much mass is reasonable for these large objects, and which is now nearly directly observed. (Information on black holes posted on the Web by NASA and other agencies is reliable, for example.)

To determine

The construction of the question by considering a supermassive black hole near the center of the galaxy and calculate the radius of a object.

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,

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

Calculation:

Problem:

A supermassive black is hole in supernova is created by the Big Bang. Calculate the radius of the black hole. (Assume the mass of the black hole is 109 times of the mass of Sun.)

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

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