Concept explainers
(a)
The Schwarzschild radius of a black hole having mass equal to that of Earth. Also calculate the density if matter is uniformly spread throughout the volume of the event horizon.
(a)
Answer to Problem 60Q
Solution:
Explanation of Solution
Given data:
A black hole having mass equal to that of Earth.
Formula used:
The expression for Schwarzschild radius of an object is given as,
Here,
The expression for density of an object is given as,
Here,
Explanation:
The mass of black hole is equal to that of earth, which is equal to
Schwarzschild radius of the black hole is calculated as follows:
Recall the expression for Schwarzschild radius of an object.
Upon substituting
Density of the black hole is calculated by considering it to be a sphere.
Recall the expression for density of an object.
Upon substituting
Substitute
Conclusion:
Hence, Schwarzschild radius of the black hole is
(b)
The Schwarzschild radius of a black hole having mass equal to that of Sun. Also calculate the density if matter is uniformly spread throughout the volume of the event horizon.
(b)
Answer to Problem 60Q
Solution:
Explanation of Solution
Given data:
A black hole having mass equal to that of Sun.
Formula used:
The expression for Schwarzschild radius of an object is given as,
Here,
The expression for density of an object is given as,
Here,
Explanation:
The mass of black hole is equal to that of Sun, which is equal to
Schwarzschild radius of the black hole is calculated as follows:
Recall the expression for Schwarzschild radius of an object.
Upon substituting
Density of the black hole is calculated by considering it to be a sphere.
Recall the expression for density of an object.
Upon substituting
Substitute
Conclusion:
Hence, Schwarzschild radius of the black hole is
(c)
The Schwarzschild radius of a black hole having mass equal to that of a supermassive black hole in NGC4261. Also calculate the density if matter is uniformly spread throughout the volume of the event horizon.
(c)
Answer to Problem 60Q
Solution:
Explanation of Solution
Given data:
A black hole having mass equal to that of a supermassive black hole in NGC4261.
Formula used:
The expression for Schwarzschild radius of an object is given as,
Here,
The expression for density of an object is given as,
Here,
Explanation:
The mass of black hole is equal to that of a supermassive black hole in NGC4261, which is equal to
Calculate Schwarzschild radius of a black hole.
Recall the expression of Schwarzschild radius of an object.
Upon substituting
Density of the black hole is calculated by considering to be a sphere.
Recall the expression for density of an object.
Upon substituting
Substitute
Conclusion:
Hence, Schwarzschild radius of the black hole is
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Chapter 21 Solutions
Universe
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