Q: The universal gravitational constant $$G$$ has a value of:

$$6.67 \times 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$}$$

Q: If two 30-kg spheres are separated by 5 meters, what is the gravitational force between them? (Use $$G = 6.67 \times 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$})$$

$$2.4 \times 10$$^{-9}$$ \ \mathrm{N}$$

Q: A 1000-kg satellite is in orbit above the Earth. At what height above Earth's surface is the gravitational force on the satellite equal to 1000 N? (Use $$G = 6.67 \times 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$}$$, $$M_E = 5.97 \times 10$$^{24}$$ \ \mathrm{kg}$$, $$R_E = 6.37 \times 10^6$ \ \mathrm{m})$$

$$1.85 \times 10^8$ \ \mathrm{m}$$

Q: Two spheres of mass 300 kg and 500 kg are placed 20 cm apart. If a third sphere of mass 200 kg is placed between them, 8 cm from the 300-kg sphere, what is the net gravitational force on the 200-kg sphere?

$$3.6 \times 10$$^{10}$$ \ \mathrm{N}$$

Q: A 2000-kg spacecraft is 1500 km above the surface of a planet the same size as Earth. If the gravitational force on the spacecraft is 18,000 N, what is the mass of the planet? (Use $$G = 6.67 \times 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$}$$, $$R_E = 6.37 \times 10^6$ \ \mathrm{m})$$

$$5.59 \times 10$$^{24}$$ \ \mathrm{kg}$$

Question 1

According to Newton's Universal Law of Gravitation, what is the correct formula for the gravitational force between two point masses $$m_1$$ and $$m_2$$ separated by a distance $$r$$?

Accepted Answer

$$F_G = \frac{G m_1$ m_2$}{r^2$}$$

Question 2

The universal gravitational constant $$G$$ has a value of:

Accepted Answer

$$6.67 	imes 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$}$$

Question 3

If two 30-kg spheres are separated by 5 meters, what is the gravitational force between them? (Use $$G = 6.67 	imes 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$})$$

Accepted Answer

$$2.4 	imes 10$$^{-9}$$ \ \mathrm{N}$$

Question 4

The gravitational force between two objects is directed along:

Accepted Answer

A line connecting the centers of mass of the two objects

Question 5

Suppose you have two spheres of mass 10 kg and 25 kg, positioned 5 m apart. If a third sphere is placed between them so that the net gravitational force on it is zero, how far from the 10 kg mass must it be placed?

Accepted Answer

$$1.25 \ \mathrm{m}$$

Question 6

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

Accepted Answer

It becomes one-fourth as large

Question 7

A 1000-kg satellite is in orbit above the Earth. At what height above Earth's surface is the gravitational force on the satellite equal to 1000 N? (Use $$G = 6.67 	imes 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$}$$, $$M_E = 5.97 	imes 10$$^{24}$$ \ \mathrm{kg}$$, $$R_E = 6.37 	imes 10^6$ \ \mathrm{m})$$

Accepted Answer

$$1.85 	imes 10^8$ \ \mathrm{m}$$

Question 8

When calculating the gravitational force between a planet and an object above its surface, which distance should you use for $$r in $$the formula $$F_G = \frac{G M m}{r^2$}$$?

Accepted Answer

The sum of the planet's radius and the object's height above the surface

Question 9

Two spheres of mass 300 kg and 500 kg are placed 20 cm apart. If a third sphere of mass 200 kg is placed between them, 8 cm from the 300-kg sphere, what is the net gravitational force on the 200-kg sphere?

Accepted Answer

$$3.6 	imes 10$$^{10}$$ \ \mathrm{N}$$

Question 10

A 2000-kg spacecraft is 1500 km above the surface of a planet the same size as Earth. If the gravitational force on the spacecraft is 18,000 N, what is the mass of the planet? (Use $$G = 6.67 	imes 10$$^{-11}$$ \ \mathrm{N \cdot m^2$ / kg^2$}$$, $$R_E = 6.37 	imes 10^6$ \ \mathrm{m})$$

Accepted Answer

$$5.59 	imes 10$$^{24}$$ \ \mathrm{kg}$$

Question 11

Which of the following best describes the role of the gravitational constant $$G in $$Newton's Law of Universal Gravitation?

Accepted Answer

It determines the strength of the gravitational force between two masses

Question 12

If the mass of one object is doubled while the distance between two objects remains the same, how does the gravitational force change?

Accepted Answer

It doubles

Question 13

Which of the following statements about gravitational force is correct?

Accepted Answer

It is always attractive and acts along the line joining the centers of mass of two objects

Question 14

A student calculates the gravitational force between two objects and gets a negative value. What is the most likely reason for this?

Accepted Answer

They made a sign error in their calculation

Question 15

Which of the following is NOT a correct use of the gravitational force formula $$F_G = \frac{G m_1$ m_2$}{r^2$}$$?

Accepted Answer

Using the distance from the surface of a planet instead of from its center

Question 16

If the gravitational force between two objects is $$F$$, what will the force be if both masses are tripled and the distance between them is doubled?

Accepted Answer

$$\frac{9}{4} F$$

Question 17

Why is the gravitational force between two everyday objects, such as two people, so small?

Accepted Answer

Because the masses are small and $$G is a $$very small constant

Question 18

A planet has twice the radius of Earth but the same mass. How does the gravitational force at its surface compare to that on Earth's surface?

Accepted Answer

It is one-fourth as strong

Question 19

Which of the following best explains why astronauts in the International Space Station appear weightless?

Accepted Answer

They are in continuous free fall around the Earth

Gravitational Forces and Newton's Law of Universal Gravitation

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