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Chapter 22: Problem 47

What is the mass in kilograms of a black hole whose Schwarzschild radius is \(11 \mathrm{~km}\) ?

Short Answer

Expert verified
The mass of the black hole is approximately \(2.48 \times 10^{30}\) kilograms.

Step by step solution

01

Understanding the Schwarzschild radius

The Schwarzschild radius (\(r_s\)) of a black hole is given by the formula \(r_s = 2GM/c^2\), where G is the gravitational constant (\(6.674 \times 10^{-11} m^3 kg^{-1} s^{-2}\)), M is the mass of the black hole, and c is the speed of light (\(3.00 \times 10^8 m/s\)). We need to solve this equation for M to find the mass of the black hole.
02

Rearrange the equation

To solve for M, we need to rearrange the equation: \(M = r_sc^2/2G\). Now we can substitute the given Schwarzschild radius and the known values for c and G into this equation.
03

Substitute and calculate

The Schwarzschild radius \(r_s\) is given as \(11 km = 11 \times 10^3 m\). Substituting all these values into the equation, we get: \(M = (11 \times 10^3 m \times (3.00 \times 10^8 m/s)^2)/ (2 \times 6.674 \times 10^{-11} m^3 kg^{-1} s^{-2})\). This gives us a result of approximately \( 2.48 \times 10^{30} kg\).

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Most popular questions from this chapter

A twenty-third-century instructor at Starfleet Academy tells her students, "If someday your starship falls into a black hole, it'll be your own fault." Explain why it would require careful piloting to direct a spacecraft into a black hole.

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