Question 1

An object at the surface of Earth (at a distance R from the center of Earth) weighs 90 N. Its weight at a distance 3R from the center of Earth is:

Accepted Answer

The gravitational force (and thus weight) is inversely proportional to the square of the distance from the center of the Earth. If the distance triples (from R to 3R), the weight decreases by a factor of 3^2 = 9. Therefore, 90 N / 9 = 10 N.

Question 2

An object is raised from the surface of Earth to a height of two Earth radii above Earth. Then:

Accepted Answer

When an object is raised above Earth's surface, its distance from the center of Earth increases. Since weight is the force of gravity acting on an object's mass, the weight of the object decreases as the distance from the center of Earth increases. However, the object's mass remains constant, as mass is an intrinsic property of the object and does not change with location. Therefore, choice C is the correct answer.

Question 3

An astronaut on the Moon simultaneously drops a feather and a hammer. The fact that they land together shows that:

Accepted Answer

This is an example of Galileo's famous experiment that demonstrated that all objects, regardless of their mass or composition, fall to the ground with the same acceleration in the absence of air resistance. The fact that the feather and hammer landed together showed that they were both falling with the same acceleration on the Moon. This is possible because the Moon has a weaker gravitational field than Earth, but in the absence of air resistance, all objects fall with the same acceleration. Therefore, option C is the best choice.

Question 4

An astronaut in an orbiting space-craft feels "weightless" because she:

Accepted Answer

An object in freefall, like an astronaut in an orbiting space-craft, experiences weightlessness because it is in a state of constant acceleration towards the center of the planet or other large object it is orbiting. The astronaut and the space-craft are both being accelerated by the gravitational pull of the planet, so they experience the same level of acceleration, making the astronaut feel weightless.

Question 5

In the formula F = Gm₁m₂/r², the quantity G:

Accepted Answer

G is a universal constant of nature, known as the gravitational constant, which relates the force of gravity between two objects to their masses and the distance between them. It is not dependent on the local value of g, is used for all masses and not just when the Earth is one of them, and is not related to the Sun in the same way that g is related to the Earth.

Question 6

Suitable units for the gravitational constant G are:

Accepted Answer

The gravitational constant G has the units of $m^3/(kg \cdot s^2)$, which matches the description in option E.

Question 7

Four particles, each with mass m, are arranged symmetrically about the origin on the x axis. A fifth particle, with mass M, is on the y axis. The direction of the gravitational force on M is:

Accepted Answer

By symmetry, the gravitational force of the four particles on the y-axis is directed towards the origin. Since M is a point mass, it will be attracted towards the center of mass of the four masses on the x-axis, which is at the origin. Therefore, the gravitational force on M is directed downwards, perpendicular to the x-axis, which corresponds to choice B ().

Question 8

Let F₁ be the magnitude of the gravitational force exerted on the Sun by Earth and F₂ be the magnitude of the force exerted on Earth by the Sun. Then:

Accepted Answer

According to Newton's third law, the magnitude of the gravitational force exerted on Earth by the Sun and that exerted on the Sun by Earth are equal in magnitude but opposite in direction. Therefore, F₁ is equal to F₂.

Question 9

If Earth were to rotate only 100 times per year about its axis:

Accepted Answer

EIf Earth rotated only 100 times a year, each day would be much longer, significantly reducing the centrifugal force experienced by objects on the Earth's surface. This reduction in centrifugal force would make our apparent weight slightly increase (C) because there's less force opposing gravity. Conversely, the reduction in centrifugal force means we wouldn't be pushed outward as strongly, so we wouldn't fly off Earth's surface (B is incorrect), nor would the atmosphere float into space due to this change (D is incorrect). Airplane flight times are more influenced by air currents than Earth's rotation speed, making A not directly relevant to the scenario. The decrease in centrifugal force also contributes to the slight increase in apparent weight, but in the context of how weight is perceived, it's more accurate to say our apparent weight would slightly decrease (E) if considering a hypothetical where centrifugal force had a more significant opposing effect to gravity, but in this context, the correct interpretation is that the decrease in centrifugal force from a slower rotation leads to an increase in apparent weight, making E incorrect based on the standard interpretation of the scenario.

Question 10

Earth exerts a gravitational force on the Moon, keeping it in its orbit. The reaction to this force, in the sense of Newton's third law, is:

Accepted Answer

Newton's third law states that every action has an equal and opposite reaction. In this case, the action is the Earth exerting a gravitational force on the Moon, and the reaction is the Moon exerting a gravitational force on Earth. Therefore, the correct answer is C. The other choices are either the result of the gravitational force (centripetal force and nearly circular orbit) or unrelated (tides and the apple hitting Newton on the head).

Question 11

The magnitude of the acceleration of a planet in orbit around the Sun is proportional to:

Accepted Answer

The answer of The magnitude of the acceleration of a...

Question 12

Venus has a mass of about 0.0558 times the mass of Earth and a diameter of about 0.381 times the diameter of Earth. The acceleration of a body falling near the surface of Venus is about:

Accepted Answer

The answer of Venus has a mass of about 0.0558...

Question 13

Let M denote the mass of Earth and let R denote its radius. The ratio g/G at Earth's surface is:

Accepted Answer

The gravitational force (F) on an object at the Earth's surface is given by F = G * (M * m) / R^2, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the object, and R is the radius of the Earth. The acceleration due to gravity (g) is given by F/m = G * M / R^2. Therefore, the ratio g/G = M / R^2, which matches the form of option B when considering the superscript and subscript notation provided.

Question 14

The gravitational constant G has the derived units

Accepted Answer

The gravitational constant G has the units of $N \cdot m^2/kg^2$, which corresponds to the option that includes meters squared on the numerator and kilograms squared on the denominator, along with the Newton (N) unit, which is the unit of force. This is the correct representation of G's units, reflecting its role in the equation for gravitational force.

Question 15

An artificial satellite of the Earth releases a bomb. Neglecting air resistance, the bomb will:

Accepted Answer

The bomb will continue to move with the same velocity and direction as the satellite at the instant of release. Since the satellite is in orbit around the Earth, both the satellite and the bomb will continue to move in a curved path around the Earth. Therefore, the bomb will never strike the Earth.

Question 16

Three particles, two with mass m and one mass M, might be arranged in any of the four configurations known below. Rank the configurations according to the magnitude of the gravitational force on M, least to greatest.

Accepted Answer

1) M and m are far apart, so the force between them is the weakest.
2) M and m are closer, so the force between them is stronger than in configuration 1.
3) In this case, all three particles are equidistant from each other, so the forces cancel out and there is no net force on M.
4) M is closest to the two particles with mass m, so the force on M is the greatest in this configuration.

Question 17

The approximate value of g at an altitude above Earth equal to one Earth diameter is:

Accepted Answer

The answer of The approximate value of g at an...

Question 18

The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth. If a person weighs 600 N on Earth, what would he weigh on this planet?

Accepted Answer

The weight of a person on any planet is given by the formula:
W = m*g, where W is the weight, m is the mass of the person, and g is the acceleration due to gravity on that planet.
Here, we are given that the mass of the hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth. The acceleration due to gravity on the hypothetical planet can be found using the formula:
g = G*(M/R^2), where G is the gravitational constant, M is the mass of the planet, and R is its radius.
Let's assume that the mass of Earth is Me and its radius is Re. Then, we have:
M = (1/100)*Me and R = (1/4)*Re.
Substituting these values, we get:
g = G*((1/100)*Me)/((1/4)*Re)^2 = (1/25)*G*(Me/Re^2)
Now, we can find the weight of the person on the hypothetical planet using the formula:
W = m*g = (600 N)/(9.81 m/s^2)*g
Substituting the value of g, we get:
W = (600 N)/(9.81 m/s^2)*(1/25)*G*(Me/Re^2) = (24/245)*G*(Me/R^2)
Finally, we can simplify this expression by noting that G*(Me/R^2) is just the acceleration due to gravity on Earth, which is 9.81 m/s^2. Therefore, we have:
W = (24/245)*9.81 m/s^2 = 0.96*9.81 N = 9.4116 N ≈ 96 N. 
Therefore, the person would weigh 96 N on this planet.

Question 19

An astronaut finishes some work on the outside of his satellite, which is in circular orbit around the Earth. He leaves his wrench outside the satellite. The wrench will:

Accepted Answer

The wrench will continue in orbit with the satellite because, according to Newton's First Law of Motion, an object in motion will remain in motion unless acted upon by an external force. In this case, there is no external force acting on the wrench to change its orbit, so it will continue to follow the same circular path as the satellite.

Question 20

The mass of an object:

Accepted Answer

The answer of The mass of an object:
...

Quiz 13: Gravitation