Question 1

According to Newton's Law of Universal 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

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

Question 2

If the mass of one object is doubled and the distance between two objects is also doubled, how does the gravitational force between them change?

Accepted Answer

It becomes the same as before.

Question 3

Which of the following best describes the direction of the gravitational force between two masses?

Accepted Answer

The force on each mass points toward the other mass.

Question 4

A satellite is in a stable circular orbit around Earth. Which of the following statements is true about the forces acting on the satellite?

Accepted Answer

The only force acting on the satellite is gravity, which acts as the centripetal force.

Question 5

What is the acceleration due to gravity $$g at $$the surface of a planet with mass $$M$$ and radius $$R$$?

Accepted Answer

$$g = \frac{G M}{R^2$}$$

Question 6

If you weigh 800 N on Earth's surface, what would your weight be at a height where the gravitational acceleration is 10% less than at the surface?

Accepted Answer

720 N

Question 7

A 70 kg astronaut orbits Earth in the International Space Station, where $$g_{orbit} \approx 8.7 \ m/s^2$. What is the gravitational force acting on the astronaut?

Accepted Answer

$$F = 609 \ N$$

Question 8

Why do astronauts in orbit feel 'weightless' even though gravity is still acting on them?

Accepted Answer

They are in free fall, accelerating toward Earth at the same rate as their spacecraft.

Question 9

If the radius of a planet is doubled but its mass remains the same, what happens to the acceleration due to gravity at its surface?

Accepted Answer

It becomes one-fourth as large.

Question 10

A geostationary satellite orbits Earth with a period of 24 hours. Which equation correctly relates the orbital radius $$r to $$the period $$T$$ and Earth's mass $$M$$?

Accepted Answer

$$r^3$$ = \frac{G M $$T^2$$}{4 \$$pi^2$$}$$

Question 11

If you can jump to a height $$h on $$Earth, how high could you jump on the Moon, where $$g_{moon} = 1.6 \ m/s^2$ and g$$_{earth} = 9.8 \ $$m/s^2$$, assuming the same initial speed?

Accepted Answer

About 6 times higher

Question 12

A 1000 kg satellite orbits Earth at a radius $$r$$ from the center. What is its orbital speed $$v$$?

Accepted Answer

$$v = \sqrt{\frac{G M}{r}}$$

Question 13

Which of the following best explains why a projectile in low Earth orbit does not fall to the ground?

Accepted Answer

It is moving forward fast enough that as it falls, the Earth's surface curves away beneath it.

Question 14

If the gravitational force between two objects is $$F$$, what will the force be if the distance between them is tripled?

Accepted Answer

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

Question 15

A planet orbits a star of mass $$M at a $$distance $$r. $$What is the period $$T of $$its orbit?

Accepted Answer

$$T = 2\pi \sqrt{\frac{r^3$}{G M}}$$

Question 16

Which of the following is a correct statement about the action-reaction pair in Newton's law of gravitation?

Accepted Answer

The force that $$m_1$$ exerts on $$m_2 is $$equal in magnitude and opposite in direction to the force that $$m_2$$ exerts on $$m_1.$$

Question 17

A satellite in a circular orbit has an apparent weight of zero. What does this mean physically?

Accepted Answer

The normal force on the satellite is zero because it is in free fall.

Question 18

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 19

Which of the following is the correct relationship between the period $$T$$ and the radius $$r$$ for a planet orbiting a star, according to Kepler's third law?

Accepted Answer

$$T^2$$ \propto $$r^3$$

Question 20

A projectile is launched horizontally from a height $$h$$ above the surface of a planet. What condition must be met for the projectile to enter a stable circular orbit around the planet?

Accepted Answer

Its tangential speed must be such that the curvature of its trajectory matches the curvature of the planet.

Circular Motion and Gravity: Study Notes

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