# 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
kg
for the mass of the Sun and
m^{3}/kg⋅s^{2}
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
kg for the mass of Earth,
m^{3}/kg⋅s^{2}
for the universal gravitational constant, and
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
m^{3}/kg⋅s^{2} for the universal gravitational constant.
Give your answer to 3 significant figures.

- A kg
- B kg
- C kg
- D kg
- E 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
m for the length of
1 AU,
m^{3}/kg⋅s^{2}
for the universal gravitational constant,
and
m/s
for the speed of light. Give your answer to 3 significant figures.

- A kg
- B kg
- C kg
- D kg
- E kg

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

- A km
- B km
- C km
- D km
- E km

**Q8: **

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

- A
- B
- C
- D
- E