22. What does it mean for a force to act in accordance with an inverse square law?

The square of the force is inversely proportional to the distance.

The force decreases if the distance increases.

The force is directly proportional to 1/r2 where r is the distance.

The force is directly proportional to the distance squared.

Question 23. 23. It takes 82 years for Uranus to circle the sun once. Approximately how far is Uranus from the sun in AU, where 1 AU is the distance of Earth from the sun?

740 AU

19 AU

82 AU

6,700 AU

Question 24. 24. Why would an observer out in space see the earth orbiting the sun rather than the sun orbiting the earth?

The sun has much more mass than the earth.

The sun's gravity pulls on the earth, rather than the earth's gravity pulling on the sun.

The same force that pulls an apple to the earth pulls the earth toward the sun.

The force of gravity decreases with distance.

Question 25. 25. What is the magnitude of the earth's gravitational field at sea level?

6.67 × 1011 N/kg

4.9 N/kg

1.0 N/kg

9.8 N/kg

The force is directly proportional to 1/r2 where r is the distance.

19 AU

9.8 N/kg

Question 22: The force is directly proportional to 1/r^2 where r is the distance. So, it's like saying "I will only give you half the candy if you stand twice as far from me."

Question 23: Uranus takes 82 years to circle the sun once, so it must really love going in circles. The distance from the sun to Uranus is approximately 19 AU. That's quite a long-distance relationship!

Question 24: An observer in space would see the earth orbiting the sun because the sun has much more mass than the earth. It's like a dance where the sun leads, and the earth follows. Just imagine the sun saying, "I've got the moves like gravity!"

Question 25: The magnitude of the earth's gravitational field at sea level is 9.8 N/kg. It's like the earth is giving a big bear hug to everything on its surface. So hold onto your hats (or your gravity boots), because we're in for a wild ride!

For question 22, the correct answer is:

The force is directly proportional to 1/r2 where r is the distance.

For question 23, the correct answer is:

19 AU

For question 24, the correct answer is:

The same force that pulls an apple to the earth pulls the earth toward the sun.

For question 25, the correct answer is:

9.8 N/kg

22. What does it mean for a force to act in accordance with an inverse square law?

The correct answer is: The force is directly proportional to 1/r^2 where r is the distance.

To understand why, you can consider the mathematical expression for an inverse square law. When a force follows an inverse square law, it means that the force is inversely proportional to the square of the distance. In other words:

Force ∝ 1/d^2

where Force is the magnitude of the force, d is the distance, and ∝ indicates proportionality.

This means that as the distance increases, the force decreases. Moreover, the force decreases at a faster rate than the distance increases because of the square term in the denominator.

In the given options, the correct answer is "The force is directly proportional to 1/r^2 where r is the distance," which matches with the definition above.

23. It takes 82 years for Uranus to circle the sun once. Approximately how far is Uranus from the sun in AU, where 1 AU is the distance of Earth from the sun?

To find the distance of Uranus from the sun, we can use the information that Uranus takes 82 years to orbit the sun once. The distance of a planet from the sun is related to the time it takes to orbit by Kepler's Third Law of Planetary Motion.

According to Kepler's Third Law:

(T1^2)/(R1^3) = (T2^2)/(R2^3)

Where T1 and T2 are the periods of the two planets, and R1 and R2 are the distances of the two planets from the sun.

Let's substitute the values we know:
T1 = 1 year (Earth's orbital period)
R1 = 1 AU (distance of Earth from the sun)
T2 = 82 years (Uranus's orbital period)
R2 = ?

Solving for R2:
(1^2)/(1^3) = (82^2)/(R2^3)
1/1 = 82^2/(R2^3)
R2^3 = (82^2)/1
R2^3 = 6724
R2 = ∛6724
R2 ≈ 18.6 AU

So, the approximate distance of Uranus from the sun in AU is 18.6 AU.

Among the given options, the closest match is "19 AU."

24. Why would an observer out in space see the earth orbiting the sun rather than the sun orbiting the earth?

The correct answer is: The same force that pulls an apple to the earth pulls the earth toward the sun.

This is because of the force of gravity. Gravity is a force that attracts objects with mass towards each other. In the case of the earth and the sun, both objects have mass, and therefore gravitational forces act on both of them.

According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Since the sun has much more mass than the earth, the gravitational force between the sun and the earth is greater than the force between the earth and the sun. As a result, the earth is pulled towards the sun, causing it to orbit around the sun.

Therefore, an observer in space would see the earth orbiting the sun because the gravitational force of the sun is stronger than the gravitational force of the earth.

25. What is the magnitude of the earth's gravitational field at sea level?

The correct answer is: 9.8 N/kg.

The magnitude of the earth's gravitational field at sea level, denoted as g, is approximately 9.8 meters per second squared (9.8 m/s^2). This value represents the acceleration due to gravity near the surface of the earth at sea level.

The value of 9.8 m/s^2 means that for every kilogram of mass on the earth's surface, it experiences a force of 9.8 Newtons (N) directed towards the center of the earth.

Among the given options, the closest match is "9.8 N/kg."