Worksheet: Black Holes

In this worksheet, we will practice calculating the Schwarzschild Radius of black holes and identifying the features of black holes.

Q1:

Which of the following is the correct description of a singularity?

  • AA singularity is any point on the event horizon of a black hole.
  • BA singularity is a high-density, spherical object that can be found at the center of a black hole and that has a nonzero radius that is smaller than that of the event horizon of the black hole.
  • CA singularity is the point on the event horizon of a black hole at which an object passes through the event horizon.
  • DA singularity is an infinitely dense point that can be found at the center of a black hole.

Q2:

Which of the following statements correctly describes what is meant by accretion when referring to black holes?

  • AAccretion is the process by which quantum mechanical information is lost when matter falls into black holes.
  • BAccretion is the process of two black holes merging. The process releases large gravitational waves that can be detected at very large distances away.
  • CAccretion is the process where, over time, a black hole gradually loses mass due to quantum mechanical effects near its event horizon.
  • DAccretion is a process where matter from a nearby star is pulled into a black hole. As the matter falls inward, it forms a hot, flat accretion disk that is aligned to the resultant angular momentum of the infalling matter.

Q3:

Calculate the Schwarzschild radius for an object that has the same mass as the Sun. Use a value of 1.99×10 kg for the mass of the Sun and 6.67×10 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures.

Q4:

Which of the following is the correct description of the event horizon of a black hole?

  • AThe event horizon is the solid outer layer of a black hole.
  • BThe event horizon is the boundary around a black hole at which the gravitational pull of the black hole becomes so great as to make escape impossible, even for light.
  • CThe event horizon is the boundary around a black hole at which the gravitational pull of the black hole becomes so great that no object with mass can escape, but light can.
  • DThe event horizon is the center of mass of the black hole.

Q5:

Calculate the Schwarzschild radius for an object that has the same mass as Earth. Use a value of 5.97×10 kg for the mass of Earth, 6.67×10 m3/kg⋅s2 for the universal gravitational constant, and 3.00×10 m/s for the speed of light. Give your answer to 3 significant figures.

Q6:

Cygnus X-1 is a black hole located in the constellation Cygnus. If the Schwarzschild radius of Cygnus X-1 is 300 km, what is its mass? Use a value of 6.67×10 m3/kg⋅s2 for the universal gravitational constant. Give your answer to 3 significant figures.

  • A4.05×10 kg
  • B3.31×10 kg
  • C1.01×10 kg
  • D2.02×10 kg
  • E1.67×10 kg

Q7:

Astronomers have observed that there is a massive, dark object at the center of our galaxy. By observing the motion of stars that orbit this massive object, they have found that it must have a radius less than 45.0 AU.

What would the mass of an object that has a Schwarzschild radius of 45.0 AU be? Use a value of 1.50×10 m for the length of 1 AU, 6.67×10 m3/kg⋅s2 for the universal gravitational constant, and 3.00×10 m/s for the speed of light. Give your answer to 3 significant figures.

  • A2.28×10 kg
  • B9.11×10 kg
  • C1.21×10 kg
  • D6.32×10 kg
  • E4.55×10 kg

The object is thought to be a black hole. From the motion of the stars around it, its mass is estimated to be 8.20×10 kg. What is the Schwarzschild radius for an object with this mass? Give your answer to 3 significant figures.

  • A3.43×10 km
  • B8.59×10 km
  • C1.22×10 km
  • D6.08×10 km
  • E2.43×10 km

Q8:

Which of the following formulas correctly shows the relation between the Schwarzschild radius of a black hole and its mass?

  • A𝑅𝑀
  • B𝑅1𝑀
  • C𝑅𝑀
  • D𝑅1𝑀
  • E𝑅𝑀

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