Question 1

If Earth had twice its present mass but it orbited at the same distance from the sun as it does now,its orbital period would be

Accepted Answer

The orbital period of a planet around the sun is determined by the distance from the sun, not by its mass, according to Kepler's third law of planetary motion. Therefore, even if Earth had twice its present mass, as long as it orbits at the same distance from the sun, its orbital period would remain 1 year.

Question 2

If you stood on a planet having a mass four times that of Earth's mass,and a radius two times that of Earth's radius,you would weigh

Accepted Answer

The gravitational force that you feel (which translates to your weight) depends on both the mass of the planet and the distance from its center (radius). The formula for gravitational force is $F = G \frac{m_1 m_2}{r^2}$, where $m_1$ and $m_2$ are the masses involved, $r$ is the distance between their centers, and $G$ is the gravitational constant. If the mass of the planet is four times that of Earth and the radius is two times that of Earth, the increase in mass would tend to make you weigh four times more, but the increase in radius would square in the denominator, making the gravitational pull four times weaker (since $2^2 = 4$). These effects cancel each other out, so you would weigh the same as you do on Earth.

Question 3

The acceleration due to gravity on Planet A is one-sixth what it is on Planet B,and the radius of the Planet A is one-fourth that of Planet B.The mass of Planet A is what fraction of the mass of Planet B?

Accepted Answer

The gravitational force (F) is given by the formula F = G * (m1*m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers. The acceleration due to gravity (g) on the surface of a planet is given by g = G * M / r^2, where M is the mass of the planet and r is its radius. Given that the acceleration due to gravity on Planet A is one-sixth that of Planet B, and the radius of Planet A is one-fourth that of Planet B, we can set up the ratio of the accelerations due to gravity on the two planets as follows: gA / gB = (G * MA / rA^2) / (G * MB / rB^2). Given that gA = 1/6 * gB and rA = 1/4 * rB, substituting these values in gives us (1/6) = (MA / MB) / (1/16), which simplifies to MA / MB = 1/96.

Question 4

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars.If g_m is the acceleration due to gravity at the surface of Mars,what is the acceleration due to gravity at the location of the satellite?

Accepted Answer

The gravitational force decreases with the square of the distance from the center of the planet. At a distance of 4 times the radius (1 radius for Mars itself + 3 radii above the surface), the acceleration is g_m/16.

Question 5

When a spacecraft is launched from the earth toward the sun,at what distance from the earth will the gravitational forces due to the sun and the earth cancel? Earth's mass is 5.97 × 10²⁴ kg,the sun's mass is 1.99 × 10³⁰ kg,and the Earth-sun distance is 1.5 × 10¹¹ m.

Accepted Answer

The gravitational force exerted on the spacecraft by the sun and the earth are given by

Fsun = Gmsunm_spacecraft/r^2          (1)

Fearth = Gmearthm_spacecraft/(R-r)^2      (2)

where G is the universal gravitational constant and r is the distance from the center of the earth to the spacecraft (the distance from the center of the sun to the spacecraft is R = 1.5 × 10^11 m).

At the point where the two forces cancel out, Fsun = Fearth.

Therefore, we have

Gmsunm_spacecraft/r^2 = Gmearthm_spacecraft/(R-r)^2

Simplifying this equation yields r = (mearth/mtotal)R = (5.97×10^24 kg)/(5.97×10^24 + 1.99×10^30 kg) × 1.5×10^11 m = 2.6 × 10^18 m.

Therefore, the best answer is (B) 2.6 × 10^18 m.

Question 6

Two planets have the same surface gravity,but planet B has twice the radius of planet A.If planet A has mass m,what is the mass of planet B?

Accepted Answer

The surface gravity of the two planets is the same, which means that their gravitational force on an object of mass m is equal. Therefore, using the formula for surface gravity g = GM/R^2 (where G is the gravitational constant), we can write:

g_A = GM/R_A^2
g_B = GM/R_B^2

Since g_A = g_B, we can set the two equations equal to each other and solve for M_B/M_A:

g_A = g_B
GM_A/R_A^2 = GM_B/R_B^2
M_B/M_A = R_B^2/R_A^2 = (2R_A)^2/R_A^2 = 4

Therefore, the mass of planet B is 4 times the mass of planet A, or 4m.

Question 7

What is the gravitational force acting on a 59-kg person due to another 59-kg person standing 2.0 m away? We can model each person as a small sphere.(G = 6.67 × 10^-11 N ∙ m²/kg²)

Accepted Answer

The gravitational force between two masses is calculated using the formula $F = G \frac{m_1 m_2}{r^2}$, where $G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2$, $m_1 = 59 \, \text{kg}$, $m_2 = 59 \, \text{kg}$, and $r = 2.0 \, \text{m}$. Plugging these values into the formula gives $F = 6.67 \times 10^{-11} \frac{(59)(59)}{(2.0)^2} = 5.8 \times 10^{-8} \, \text{N}$.

Question 8

A spaceship is traveling to the Moon.At what point is it beyond the pull of Earth's gravity?

Accepted Answer

It is impossible for an object to completely escape the pull of Earth's gravity. Even objects like spacecrafts that travel far from Earth are still affected by its gravity, albeit to a lesser extent. This is why spacecrafts need continuous propulsion to maintain their course and speed towards the Moon or any other celestial object.

Question 9

Two small balls,A and B,attract each other gravitationally with a force of magnitude F.If we now double both masses and the separation of the balls,what will now be the magnitude of the attractive force on each one?

Accepted Answer

The gravitational force between two masses is given by $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the separation between the centers of the two masses. If both masses are doubled ($2m_1$ and $2m_2$) and the separation is also doubled ($2r$), the new force $F'$ can be calculated as $F' = G\frac{(2m_1)(2m_2)}{(2r)^2}$. Simplifying this gives $F' = G\frac{4m_1m_2}{4r^2} = G\frac{m_1m_2}{r^2} = F$, meaning the force remains the same.

Question 10

Two planets have the same surface gravity,but planet B has twice the mass of planet A.If planet A has radius r,what is the radius of planet B?

Accepted Answer

The answer of Two planets have the same surface gravity,but...

Question 11

The reason an astronaut in an earth satellite feels weightless is that

Accepted Answer

The sensation of weightlessness experienced by an astronaut in an earth satellite is due to the fact that they are in freefall, just like any other object orbiting the earth. The gravitational force of the earth is still acting upon the astronaut, but so is the inertia from their forward motion. This creates a state of continuous freefall, resulting in the feeling of weightlessness.

Question 12

Two small objects,with masses m and M,are originally a distance r apart,and the gravitational force on each one has magnitude F.The second object has its mass changed to 2M,and the distance is changed to r/4.What is the magnitude of the new gravitational force?

Accepted Answer

The gravitational force is given by Newton's law of gravitation: F = G(m1*m2)/r^2. Initially, F = G(m*M)/r^2. When the second mass is changed to 2M and the distance to r/4, the new force F' = G(m*2M)/(r/4)^2 = G(m*2M)/(r^2/16) = 32G(m*M)/r^2 = 32F.

Question 13

As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon),how large is the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 × 10²² kg,the distance to the Moon is 3.82 × 10⁸ m,and G = 6.67 × 10^-11 N ∙ m²/kg².

Accepted Answer

The gravitational force can be calculated using Newton's law of universal gravitation: F = G * (m1 * m2) / r^2. Substituting the given values: F = (6.67 × 10^-11) * (70 * 7.35 × 10^22) / (3.82 × 10^8)^2, which results in approximately 0.0024 N.

Question 14

Two small objects,with masses m and M,are originally a distance r apart,and the magnitude of the gravitational force on each one is F.The masses are changed to 2m and 2M,and the distance is changed to 4r.What is the magnitude of the new gravitational force?

Accepted Answer

The answer of Two small objects,with masses m and M,are...

Question 15

Satellite A has twice the mass of satellite B,and moves at the same orbital distance from Earth as satellite B.Compare the speeds of the two satellites.

Accepted Answer

The orbital speed of a satellite is determined by the gravitational pull of the Earth and its distance from the Earth, not by its own mass. Therefore, if two satellites are at the same orbital distance from Earth, they will have the same speed regardless of their masses.

Question 16

Suppose our sun had 4 times its present mass but the earth orbited it at the same distance as it presently does.What would be the length of the year on the earth under those conditions?

Accepted Answer

According to Kepler's third law, the square of the orbital period is proportional to the cube of the semi-major axis of its orbit divided by the mass of the sun. If the sun's mass is quadrupled, the orbital period would be reduced by a factor of √4, which is 2, making the year half as long.

Question 17

Planet A has twice the mass of Planet B.From this information,what can we conclude about the acceleration due to gravity at the surface of Planet A compared to that at the surface of Planet B?

Accepted Answer

The acceleration due to gravity is determined not only by the mass of a planet but also by its radius. Without knowing the radii of the two planets, we cannot accurately compare the accelerations due to gravity on their surfaces.

Question 18

A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth.What is the acceleration due to gravity on the planet in terms of g,the acceleration due to gravity at the surface of the earth?

Accepted Answer

The acceleration due to gravity on a planet is given by the formula: 
g = G M/R^2 
where G is the universal gravitational constant, M is the mass of the planet, and R is its radius. 
Comparing the planet with Earth: 
Mass of the planet, M = (1/2) Mass of Earth, Me 
Radius of the planet, R = 2 Radius of Earth, Re 
Putting the values in the formula: 
g = G (1/2) Me / (2Re)^2 
g = G Me / (2^2 x Re^2 x 2) 
g = G Me / (8 x Re^2) 
g = (1/8) G Me / Re^2 
g/8 = G M/R^2 
Therefore, the acceleration due to gravity on the planet is g/8 or (D).

Question 19

An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth.Compared to its weight on Earth,the weight of this debris is

Accepted Answer

The gravitational force (weight) decreases with the square of the distance from the center of the Earth. At two Earth radii from the center, the distance is doubled, so the weight is (1/2)^2 = 1/4 of its weight on the surface of the Earth.

Question 20

Mithra is an unknown planet that has two moons,A and B,in circular orbits around it.The table summarizes the hypothetical data about these moons.What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? (G = 6.67 × 10^-11 N ∙ m²/kg²)

Accepted Answer

The answer of 
Mithra is an unknown planet that has...

Quiz 12: Gravity

If Earth had twice its present mass but it orbited at the same distance from the sun as it does now,its orbital period would be

If you stood on a planet having a mass four times that of Earth's mass,and a radius two times that of Earth's radius,you would weigh

The acceleration due to gravity on Planet A is one-sixth what it is on Planet B,and the radius of the Planet A is one-fourth that of Planet B.The mass of Planet A is what fraction of the mass of Planet B?

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars.If g_m is the acceleration due to gravity at the surface of Mars,what is the acceleration due to gravity at the location of the satellite?

When a spacecraft is launched from the earth toward the sun,at what distance from the earth will the gravitational forces due to the sun and the earth cancel? Earth's mass is 5.97 × 10²⁴ kg,the sun's mass is 1.99 × 10³⁰ kg,and the Earth-sun distance is 1.5 × 10¹¹ m.

Two planets have the same surface gravity,but planet B has twice the radius of planet A.If planet A has mass m,what is the mass of planet B?

What is the gravitational force acting on a 59-kg person due to another 59-kg person standing 2.0 m away? We can model each person as a small sphere.(G = 6.67 × 10^-11 N ∙ m²/kg²)

A spaceship is traveling to the Moon.At what point is it beyond the pull of Earth's gravity?

Two small balls,A and B,attract each other gravitationally with a force of magnitude F.If we now double both masses and the separation of the balls,what will now be the magnitude of the attractive force on each one?

Two planets have the same surface gravity,but planet B has twice the mass of planet A.If planet A has radius r,what is the radius of planet B?

The reason an astronaut in an earth satellite feels weightless is that

Two small objects,with masses m and M,are originally a distance r apart,and the gravitational force on each one has magnitude F.The second object has its mass changed to 2M,and the distance is changed to r/4.What is the magnitude of the new gravitational force?

As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon) ,how large is the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 × 10²² kg,the distance to the Moon is 3.82 × 10⁸ m,and G = 6.67 × 10^-11 N ∙ m²/kg².

Two small objects,with masses m and M,are originally a distance r apart,and the magnitude of the gravitational force on each one is F.The masses are changed to 2m and 2M,and the distance is changed to 4r.What is the magnitude of the new gravitational force?

Satellite A has twice the mass of satellite B,and moves at the same orbital distance from Earth as satellite B.Compare the speeds of the two satellites.

Suppose our sun had 4 times its present mass but the earth orbited it at the same distance as it presently does.What would be the length of the year on the earth under those conditions?

Planet A has twice the mass of Planet B.From this information,what can we conclude about the acceleration due to gravity at the surface of Planet A compared to that at the surface of Planet B?

A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth.What is the acceleration due to gravity on the planet in terms of g,the acceleration due to gravity at the surface of the earth?

An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth.Compared to its weight on Earth,the weight of this debris is

Mithra is an unknown planet that has two moons,A and B,in circular orbits around it.The table summarizes the hypothetical data about these moons.What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? (G = 6.67 × 10^-11 N ∙ m²/kg²)

Quiz 12: Gravity

If Earth had twice its present mass but it orbited at the same distance from the sun as it does now,its orbital period would be

If you stood on a planet having a mass four times that of Earth's mass,and a radius two times that of Earth's radius,you would weigh

The acceleration due to gravity on Planet A is one-sixth what it is on Planet B,and the radius of the Planet A is one-fourth that of Planet B.The mass of Planet A is what fraction of the mass of Planet B?

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars.If gm is the acceleration due to gravity at the surface of Mars,what is the acceleration due to gravity at the location of the satellite?

When a spacecraft is launched from the earth toward the sun,at what distance from the earth will the gravitational forces due to the sun and the earth cancel? Earth's mass is 5.97 × 1024 kg,the sun's mass is 1.99 × 1030 kg,and the Earth-sun distance is 1.5 × 1011 m.

Two planets have the same surface gravity,but planet B has twice the radius of planet A.If planet A has mass m,what is the mass of planet B?

What is the gravitational force acting on a 59-kg person due to another 59-kg person standing 2.0 m away? We can model each person as a small sphere.(G = 6.67 × 10-11 N ∙ m2/kg2)

A spaceship is traveling to the Moon.At what point is it beyond the pull of Earth's gravity?

Two small balls,A and B,attract each other gravitationally with a force of magnitude F.If we now double both masses and the separation of the balls,what will now be the magnitude of the attractive force on each one?

Two planets have the same surface gravity,but planet B has twice the mass of planet A.If planet A has radius r,what is the radius of planet B?

The reason an astronaut in an earth satellite feels weightless is that

Two small objects,with masses m and M,are originally a distance r apart,and the gravitational force on each one has magnitude F.The second object has its mass changed to 2M,and the distance is changed to r/4.What is the magnitude of the new gravitational force?

As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon) ,how large is the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 × 1022 kg,the distance to the Moon is 3.82 × 108 m,and G = 6.67 × 10-11 N ∙ m2/kg2.

Two small objects,with masses m and M,are originally a distance r apart,and the magnitude of the gravitational force on each one is F.The masses are changed to 2m and 2M,and the distance is changed to 4r.What is the magnitude of the new gravitational force?

Satellite A has twice the mass of satellite B,and moves at the same orbital distance from Earth as satellite B.Compare the speeds of the two satellites.

Suppose our sun had 4 times its present mass but the earth orbited it at the same distance as it presently does.What would be the length of the year on the earth under those conditions?

Planet A has twice the mass of Planet B.From this information,what can we conclude about the acceleration due to gravity at the surface of Planet A compared to that at the surface of Planet B?

A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth.What is the acceleration due to gravity on the planet in terms of g,the acceleration due to gravity at the surface of the earth?

An piece of space debris is released from rest at an altitude that is two earth radii from the center of the earth.Compared to its weight on Earth,the weight of this debris is

Mithra is an unknown planet that has two moons,A and B,in circular orbits around it.The table summarizes the hypothetical data about these moons.What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? (G = 6.67 × 10-11 N ∙ m2/kg2)

A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars.If g_m is the acceleration due to gravity at the surface of Mars,what is the acceleration due to gravity at the location of the satellite?

When a spacecraft is launched from the earth toward the sun,at what distance from the earth will the gravitational forces due to the sun and the earth cancel? Earth's mass is 5.97 × 10²⁴ kg,the sun's mass is 1.99 × 10³⁰ kg,and the Earth-sun distance is 1.5 × 10¹¹ m.

What is the gravitational force acting on a 59-kg person due to another 59-kg person standing 2.0 m away? We can model each person as a small sphere.(G = 6.67 × 10^-11 N ∙ m²/kg²)

As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon) ,how large is the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 × 10²² kg,the distance to the Moon is 3.82 × 10⁸ m,and G = 6.67 × 10^-11 N ∙ m²/kg².

Mithra is an unknown planet that has two moons,A and B,in circular orbits around it.The table summarizes the hypothetical data about these moons.What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? (G = 6.67 × 10^-11 N ∙ m²/kg²)