Question 1

Which of the following statements best describes Newton's Law of Universal Gravitation?

Accepted Answer

It states that every particle of matter attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Question 2

A satellite orbits Earth in a circular path at a constant altitude. Which equation gives the speed $$v$$ required for a stable circular orbit at radius $$r$$ from Earth's center (mass $$M_E$$)?

Accepted Answer

$$v = \sqrt{\dfrac{GM_E}{r}}$$

Question 3

If the gravitational force between two masses is 100 N when they are separated by 6 m, what will the force be if the separation is reduced to 3 m?

Accepted Answer

400 N

Question 4

Which of the following is true about the gravitational force between two spherically symmetric bodies?

Accepted Answer

It acts as if all the mass of each body were concentrated at the center of mass.

Question 5

A 70 kg astronaut is in orbit 400 km above Earth's surface. Given Earth's radius $$R_E = 6.38 	imes 10^6$ m and mass M_E = 5.98$$ 	imes $$10^{24} kg$$, what is the astronaut's weight in orbit? (Use $$G = 6.67 	imes 10$$^{-11}$$ N m^2$/kg^2$)

Accepted Answer

About 640 N

Question 6

Which of the following best explains why astronauts in orbit experience apparent weightlessness?

Accepted Answer

Because both the astronauts and the satellite are in free fall, accelerating toward Earth at the same rate.

Question 7

The gravitational potential energy $$U of a $$system consisting of a mass $$m$$ and the Earth (mass $$M_E) $$separated by distance $$r is $$given by:

Accepted Answer

$$U = -GmM_E/r$$

Question 8

Which of the following is a consequence of Kepler's Second Law?

Accepted Answer

Planets sweep out equal areas in equal times, so they move faster when closer to the Sun.

Question 9

What is the escape velocity $$v_{esc}$$ from the surface of a planet of mass $$M$$ and radius $$R$$?

Accepted Answer

$$v_{esc} = \sqrt{\dfrac{2GM}{R}}$$

Question 10

The gravitational constant $$G$$ was first measured by Henry Cavendish using which experimental method?

Accepted Answer

A torsion balance measuring the force between lead spheres.

Question 11

A satellite is placed at a Lagrange point between the Earth and the Sun where the net gravitational force is zero. Which equation must be satisfied for the satellite's position $$r$$ from Earth (distance between Earth and Sun is $$D$$)?

Accepted Answer

$$\dfrac{GM_{Earth}}{r^2$} = \dfrac{GM_{Sun}}{(D - r)^2$}$$

Question 12

Which of the following best describes the Schwarzschild radius of a black hole?

Accepted Answer

It is the radius at which the escape velocity equals the speed of light.

Question 13

On the surface of Mars, the acceleration due to gravity $$g_{Mars} is $$given by $$g_{Mars} = \dfrac{GM_{Mars}}{R_{Mars}^2}. If$$ $$M_{Mars} = 6.42 	imes 10$$^{23}$$ kg and R$$_{Mars} = 3.38 	imes $$10^6 m$$, what is $$g_{Mars}$$?

Accepted Answer

3.75 m/s$$^2$$

Question 14

Which of the following is true about gravitational potential energy near Earth's surface for a small height $$h$$ above the surface?

Accepted Answer

$$U \approx mgh$$

Question 15

If the mass of the Earth were doubled, but its radius remained the same, how would the acceleration due to gravity $$g at $$the surface change?

Accepted Answer

It would be doubled.

Question 16

Which of the following is a correct statement about the gravitational force between two objects?

Accepted Answer

It is always attractive and acts along the line joining their centers of mass.

Question 17

A planet moves in an elliptical orbit around the Sun. According to Kepler's laws, what happens to its speed as it moves closer to the Sun?

Accepted Answer

It increases.

Question 18

Which of the following is a real-world method for detecting black holes?

Accepted Answer

Looking for x-rays emitted from accretion disks around black holes.

Question 19

If the distance between two masses is tripled, how does the gravitational force between them change?

Accepted Answer

It becomes nine times smaller.

Chapter 13: Gravitation – Study Notes

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