Question 1

Which of the following best describes Newton's law of universal gravitation?

Accepted Answer

Every particle of matter attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them: $$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 2

A satellite is in a stable circular orbit around Earth. Which force provides the necessary centripetal acceleration?

Accepted Answer

The gravitational force between the satellite and the Earth

Question 3

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

Accepted Answer

It would be doubled: $$g' = 2g$$

Question 4

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

Accepted Answer

The force is equal in magnitude and opposite in direction for both objects.

Question 5

An astronaut on the Moon weighs less than on Earth because:

Accepted Answer

The Moon has a smaller radius and lower mass than Earth, resulting in a lower gravitational acceleration.

Question 6

What is the escape speed $$v_{esc}$$ from the surface of the Earth, given $$M_E = 5.97 	imes 10$$^{24}$$ kg and R_E = 6.37$$ 	imes $$10^6 m$$?

Accepted Answer

$$v_{esc} = \sqrt{\frac{2GM_E}{R_E}}$$

Question 7

Kepler's first law states that:

Accepted Answer

Each planet moves in an elliptical orbit with the sun at one focus.

Question 8

According to Kepler's second law, a planet moves fastest in its orbit when:

Accepted Answer

It is closest to the sun (perihelion).

Question 9

The gravitational potential energy $$U of a $$mass $$m at a $$distance $$r$$ from the center of the Earth is:

Accepted Answer

$$U = -G \frac{M_E m}{r}$$

Question 10

If a point mass is inside a spherically symmetric shell, what is the net gravitational force exerted on it by the shell?

Accepted Answer

It is zero.

Question 11

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

Accepted Answer

They are falling freely with the satellite, experiencing no normal force.

Question 12

Kepler's third law relates the orbital period $$T of a $$planet to the semi-major axis $$a of $$its orbit. Which equation expresses this law for a planet orbiting the sun?

Accepted Answer

$$T = 2\pi \sqrt{\frac{a^3$}{GM_S}}$$

Question 13

A comet's tail always points away from the sun because:

Accepted Answer

Solar wind and radiation pressure push the evaporated material away from the sun.

Question 14

The Schwarzschild radius $$R_S of a $$black hole of mass $$M is $$given by:

Accepted Answer

$$R_S = \frac{2GM}{c^2$}$$

Question 15

Why does the weight of an object decrease with altitude above Earth's surface?

Accepted Answer

Because the gravitational force decreases as the distance from Earth's center increases.

Question 16

If the Earth's radius were to increase while its mass remained constant, what would happen to the acceleration due to gravity at the surface?

Accepted Answer

It would decrease.

Question 17

Which of the following is a method used to detect black holes?

Accepted Answer

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

Question 18

The center of mass of a planet-star system is located:

Accepted Answer

At a point between the planet and the star, closer to the more massive body.

Question 19

Which of the following is true about the gravitational potential energy of the earth-astronaut system as the astronaut moves away from Earth?

Accepted Answer

It becomes less negative (increases).

Question 20

A projectile is launched from Earth's surface. What determines whether it will escape Earth's gravity or remain in orbit?

Accepted Answer

Its initial speed relative to the escape velocity.

Chapter 13: Gravitation – Structured Study Notes

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