   Chapter 34, Problem 22PE

Chapter
Section
Textbook Problem

What is the Schwarzschild radius of a blank hole that has a mass eight times that of our Sun? Note that stars must be more massive than the Sun to form black holes as a result of a supernova.

To determine

The Schwarzschild radius of a black hole having a mass which is eight times of the sun.

Explanation

Given:

Mass of sun, ms=1.989×1030kg

Speed of light, c=3×108m/s

Gravitational constant, G=6.67×1011N-m2/kg2

Formula used:

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

Rsc=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 eight times the mass of the sun.

Calculate the mass of the black hole.

m=8ms

Substitute 1.989×1030kg for ms in the above expression.

m=8×1.989×1030kg=15.91×1030kg

Substitute 15

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