Question 1

Which of the following best describes the direction of the gravitational force between two masses $$m_1$$ and $$m_2$$?

Accepted Answer

It acts along the line joining the two masses, always attractive.

Question 2

Given two supertankers, each with a mass of $$1.0 	imes 10^8$ kg, separated by 20$ m, what is the magnitude of the gravitational force between them? Use G = 6.67$$ 	imes $$10^{-11} kg$^{-1} m$^3 s$^{-2}.$$

Accepted Answer

$$1.67 N$$

Question 3

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

Accepted Answer

It becomes one-fourth as large.

Question 4

Which principle allows you to find the total gravitational force on a mass due to multiple other masses?

Accepted Answer

The principle of superposition

Question 5

A satellite of mass $$m$$ orbits a planet of mass $$M in a $$circular orbit of radius $$r. $$Which equation gives the orbital speed $$v of $$the satellite?

Accepted Answer

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

Question 6

The period $$T of a $$planet in a circular orbit of radius $$r$$ around a star of mass $$M is $$given by:

Accepted Answer

$$T = \sqrt{\dfrac{4\pi^2$ r^3$}{GM}}$$

Question 7

What is the acceleration due to gravity $$g at a $$distance $$r$$ from the center of a planet of mass $$M$$?

Accepted Answer

$$g = \dfrac{GM}{r^2$}$$

Question 8

If you move from the surface of the Earth to a height where you are twice as far from the center of the Earth, what happens to your weight?

Accepted Answer

It becomes one-fourth as large.

Question 9

Which of the following is NOT a statement of Kepler’s Laws?

Accepted Answer

The force between two planets is inversely proportional to the square of the distance between them.

Question 10

A person of mass $$70 kg $$stands on the surface of Mars ($$m_{mars} = 6.4 	imes 10$$^{23}$$ kg, r$$_{mars} = 3.4 	imes $$10^6 m). $$What is their weight on Mars? ($$G = 6.67 	imes 10$$^{-11}$$ kg$$^{-1}$$ m^3$ s$$^{-2}$$)

Accepted Answer

$$260 N$$

Question 11

Why do the gravitational forces $$F_{12}$$ and $$F_{21}$$ between two masses have equal magnitude?

Accepted Answer

Because of Newton’s third law of motion.

Question 12

A satellite is in a circular orbit $$400 km $$above the Earth's surface ($$r_{earth} = 6.4 	imes 10^6$ m). What is the approximate acceleration due to gravity at this altitude?

Accepted Answer

$$8.7 m/s$^2$$

Question 13

Which of the following best describes Kepler’s Second Law?

Accepted Answer

A line joining a planet and the Sun sweeps out equal areas in equal times.

Question 14

If the mass of the Earth were doubled but its radius remained the same, what would happen to the acceleration due to gravity at the surface?

Accepted Answer

It would double.

Question 15

A planet orbits the Sun in an elliptical path. At which point in its orbit does it move fastest?

Accepted Answer

At the closest point to the Sun (perihelion).

Question 16

Which of the following is a correct expression for the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by a distance $$r$$?

Accepted Answer

$$F = G \dfrac{m_1$ m_2$}{r^2$}$$

Question 17

A student claims that the acceleration due to gravity is the same everywhere on Earth. Which of the following best evaluates this claim?

Accepted Answer

Incorrect, because $$g$$ decreases with altitude and varies with latitude.

Gravitational Force, Orbits, and Kepler’s Laws

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