Deck 12: Gravity

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

A)4 years.
B)3 years.
C)2 years.
D)1 year.
E)6 months.

Answer 1

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

A)the same as you do on Earth.
B)two times more than you do on Earth.
C)two times less than you do on Earth.
D)four times more than you do on Earth.

Answer 2

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?

A)1/6
B)1/16
C)1/24
D)1/96
E)1/12

Answer 3

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?

A)g_m/9
B)0
C)g_m
D)g_m/3
E)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.

A)1.3 × 10⁸ m
B)2.6 × 10⁸ m
C)1.3 × 10¹⁰ m
D)2.6 × 10¹⁰ 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?

A)m/
B)m
C)m
D)4m
E)m/4

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)

A)5.8 × 10^-8 _N
B)8.5 × 10³ _N
C)1.2 × 10^-7 _N
D)9.8 × 10^-10 _N
E)2.0 × 10^-9 _N

Question 8

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

A)when it gets above the atmosphere
B)when it is half-way there
C)when it is closer to the Moon than it is to Earth
D)It is never beyond the pull of Earth's gravity.

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?

A)16F
B)8F
C)4F
D)F
E)F/4

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?

A)r/
B)r
C)r
D)4r
E)2r

Question 11

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

A)the astronaut is beyond the range of the earth's gravity.
B)the astronaut is falling.
C)the astronaut is at a point in space where the effects of the moon's gravity and the earth's gravity cancel.
D)this is a psychological effect associated with rapid motion.
E)the astronaut's acceleration is zero.

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?

A)F/32
B)F/16
C)16F
D)32F
E)2F

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.

A)0.24 N
B)0.024 N
C)0.0024 N
D)0.00024 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?

A)F/16
B)F/4
C)16F
D)4F
E)F/2

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.

A)The speed of B is twice the speed of A.
B)The speed of B is one-half the speed of A.
C)The speed of B is one-fourth the speed of A.
D)The speed of B is equal to the speed of A.
E)The speed of B is four times the speed of A.

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?

A)1/4 as long as the present year
B)1/2 as long as the present year
C)the same as the present year
D)twice as long as the present year
E)four times as long as the present year

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?

A)The acceleration due to gravity on Planet A must be twice as great as the acceleration due to gravity on Planet B.
B)The acceleration due to gravity on Planet A must be four times as great as the acceleration due to gravity on Planet B.
C)The acceleration due to gravity on Planet A is the same as the acceleration due to gravity on Planet B.
D)The acceleration due to gravity on Planet A is greater than the acceleration due to gravity on Planet B,but we cannot say how much greater.
E)We cannot conclude anything about the acceleration due to gravity on Planet A without knowing the radii of the two planets.

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?

A)g
B)g/2
C)g/4
D)g/8
E)g/16

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

A)zero.
B)the same as on the surface of the earth.
C)one-half of its weight on the surface of the earth.
D)one-third of its weight on the surface of the earth.
E)one-quarter 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)

A)1.6 × 10¹³ N
B)4.4 × 10¹³ N
C)1.0 × 10¹⁴ N
D)2.0 × 10¹⁴ N
E)4.0 × 10¹⁴ N

Question 21

What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius?

A)580 N
B)290 N
C)1160 N
D)2320 N
E)1200 N

Question 22

The mass of Pluto is 1.31 × 10²² kg and its radius is 1.15 × 10⁶ m.What is the acceleration of a freely-falling object at the surface of Pluto if it has no atmosphere? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)0.661 m/s²
B)9.81 m/s²
C)1.62 m/s²
D)3.72 m/s²
E)0.140 m/s²

Question 23

An astronaut goes out for a "space-walk" at a distance above the earth equal to the radius of the earth.What is her acceleration due to gravity at that point?

A)zero
B)g
C)g/2
D)g/4
E)g/

Question 24

Mithra is an unknown planet that has two airless moons,A and B,in circular orbits around it.The table summarizes the hypothetical data about these moons.If you dropped a laser at the surface of Moon B,at what rate would it accelerate toward the ground? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)0.10 m/s²
B)0.15 m/s²
C)0.20 m/s²
D)0.25 m/s²
E)0.30 m/s²

Question 25

Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth.With g representing,as usual,the acceleration due to gravity at the surface of Earth,the acceleration due to gravity at the surface of Z-34 is

A)g/3.
B)3g.
C)6g.
D)g/9.
E)9g.

Question 26

A spaceship with a mass of 2.8 × 10⁶ kg is traveling toward two spherical asteroids,each with a mass of 5.0 × 10¹⁶ kg,that are 40 km apart center-to-center.Its path is perpendicular to the line joining the asteroids and is aimed at the midpoint of that line.What is the net gravitational force exerted by the asteroids on the spaceship when the spaceship is 30 km away from that midpoint? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)12,000 N
B)8,000 N
C)16,000 N
D)6,200 N
E)18,000 N

Question 27

The radius of the earth is R.At what distance above the earth's surface will the acceleration of gravity be 4.9 m/s²?

A)0.41 R
B)0.50 R
C)1.00 R
D)1.41 R
E)0.25 R

Question 28

The mass of the Moon is 7.4 × 10²² kg,its radius is 1.74 × 10³ km,and it has no atmosphere.What is the acceleration due to gravity at the surface of the Moon? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)2.8 × 10⁶ m/s²
B)9.8 m/s²
C)4.9 m/s²
D)1.6 m/s²
E)0.80 m/s²

Question 29

At a distance of 14,000 km from the center of Planet Z-99,the acceleration due to gravity is 32 m/s².What is the acceleration due to gravity at a point 28,000 km from the center of this planet?

A)8.0 m/s²
B)16 m/s²
C)128 m/s²
D)4.0 m/s²
E)2.0 m/s²

Question 30

At a given point above Earth's surface,the acceleration due to gravity is equal to
What is the altitude of this point above Earth's surface? (G = 6.67 × 10^-11 N ∙ m²/kg²,M_earth = 5.97 × 10²⁴ kg,R_earth = 6.38 × 10⁶ m)

A)770 km
B)970 km
C)1,500 km
D)2,000 km
E)2,400 km

Question 31

What would be the weight of a 59.1-kg astronaut on a planet twice as massive as Earth and having twice Earth's radius?

A)580 N
B)290 N
C)1160 N
D)118 N
E)1200 N

Question 32

From what height above the surface of the earth should an object be dropped to initially experience an acceleration of 0.54g? (G = 6.67 × 10^-11 N ∙ m²/kg²,M_earth = 5.97 × 10²⁴ kg,R_earth = 6.38 × 10⁶ m)

A)2300 km
B)1700 km
C)5400 km
D)2900 km

Question 33

At their closest approach,Venus and Earth are 4.20 × 10¹⁰ m apart.The mass of Venus is 4.87 × 10²⁴ kg,the mass of Earth is 5.97 × 10²⁴ kg,and G = 6.67 × 10^-11 N ∙ m²/kg².What is the magnitude of the gravitational force exerted by Venus on Earth at that point?

A)1.10 × 10¹⁸ N
B)4.62 × 10²⁸ N
C)5.43 × 10²⁶ N
D)6.30 × 10²⁰ N
E)1.72 × 10¹⁹ N

Question 34

The earth has radius R.A satellite of mass 100 kg is in orbit at an altitude of 3R above the earth's surface.What is the satellite's weight at the altitude of its orbit?

A)61 N
B)110 N
C)9000 N
D)16,000 N

Question 35

An object weighs 432 N on the surface of the earth.The earth has radius R.If the object is raised to a height of 3R above the earth's surface,what is its weight?

A)108 N
B)48.0 N
C)27.0 N
D)305 N
E)144 N

Question 36

In another solar system,a planet has an airless moon Zygo that is 4.0 × 10⁵ m in diameter.Experiments reveal that a freely falling object at the surface of Zygo accelerates at 0.20 m/s².What is the mass of Zygo? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)2.4 × 10¹⁹ kg
B)4.8 × 10¹⁹ kg
C)1.2 × 10²⁰ kg
D)2.4 × 10²⁰ kg
E)4.8 × 10²⁰ kg

Question 37

By how many newtons does the weight of a 100-kg person decrease when he goes from sea level to mountain top at an altitude of 5000 m? The mean radius of the earth is 6.38 × 10⁶ m.

A)0.60 N
B)1.5 N
C)2.6 N
D)3.6 N
E)9.8 N

Question 38

What is the distance from the center of the Moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is 5.97 × 10²⁴ kg,the mass of the Moon is 7.35 × 10²² kg,the center-to-center distance between Earth and the Moon is 3.84 × 10⁸ m,and G = 6.67 × 10^-11 N ∙ m²/kg².

A)3.45 × 10⁸ m
B)3.84 × 10⁷ m
C)4.69 × 10⁶ m
D)3.83 × 10⁶ m
E)4.69 × 10⁷ m

Question 39

An astronaut drops a marble on the surface of the airless Planet Z-49 and observes that it takes 1.02 s for the marble to fall 2.00 m starting from rest.She also knows that the radius of Z-49 is 3.39 × 10⁶ m.From this information,what will she determine for the mass of Z-49? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)3.30 × kg.
B)6.62 × kg.
C)4.62 × kg.
D)8.09 × kg.
E)9.95 × kg.

Question 40

Three identical 50-kg balls are held at the corners of an equilateral triangle,30 cm on each side.If one of the balls is released,what is the magnitude of its initial acceleration if the only forces acting on it are the gravitational forces due to the other two masses? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)3.7 × 10^-8 m/s²
B)2.5 × 10^-8 m/s²
C)1.9 × 10^-8 m/s²
D)4.2 × 10^-8 m/s²
E)6.4 × 10^-8 m/s²

Question 41

Suppose NASA wants a satellite to revolve around Earth 5 times a day.What should be the radius of its orbit if we neglect the presence of the Moon? (G = 6.67 × 10^-11 N ∙ m²/kg²,M_earth = 5.97 × 10²⁴ kg)

A)1.44 × 10⁷ m
B)0.69 × 10⁷ m
C)7.22 × 10⁷ m
D)2.11 × 10⁷ m

Question 42

A satellite that is in a circular orbit 230 km above the surface of the planet Zeeman-474 has an orbital period of 89 min.The radius of Zeeman-474 is 6.38 × 10⁶ m.What is the mass of this planet? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)5.0 × 10²⁴ kg
B)5.5 × 10²⁴ kg
C)6.0 × 10²⁴ kg
D)6.5 × 10²⁴ kg

Question 43

Find the orbital speed of an ice cube in the rings of Saturn.The mass of Saturn is 5.68 x 10²⁶ kg,and use an orbital radius of 1.00 x 10⁵ km.(G = 6.67 × 10^-11 N ∙ m²/kg²)

A)19.5 km/s
B)27.5 km/s
C)13.8 km/s

Question 44

A satellite having orbital speed V orbits a planet of mass M.If the planet had half as much mass,the orbital speed of the satellite at the same distance from the center would be

A)V .
B)2V.
C)V.
D)V/ .
E)V/2.

Question 45

A spherically symmetric planet has four times the earth's mass and twice its radius.If a jar of peanut butter weighs 12 N on the surface of the Earth,how much would it weigh on the surface of this planet?

A)3.0 N
B)6.0 N
C)12 N
D)24 N
E)36 N

Question 46

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 mass of Mithra? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)1 × 10²² kg
B)3 × 10²² kg
C)1 × 10²³ kg
D)3 × 10²³ kg
E)1 × 10²⁴ kg

Question 47

Asteroid Ida was photographed by the Galileo spacecraft in 1993,and the photograph revealed that the asteroid has a small moon,which has been named Dactyl.From the dimensions of Ida and its general features,one can estimate the mass of Ida to be 4.5 × 10¹⁶ kg,and the distance between Dactyl and Ida is approximately 90 km.Assuming a circular orbit,what would be the orbital speed of Dactyl? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)5.8 m/s
B)11 m/s
C)2.3 m/s
D)2.9 m/s
E)30 m/s

Question 48

The innermost satellite of Jupiter orbits the planet with a radius of 422 × 10³ km and a period of 1.77 days.What is the mass of Jupiter? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)1.33 × 10²⁷ kg
B)1.50 × 10²⁷ kg
C)1.72 × 10²⁷ kg
D)1.89 × 10²⁷ kg
E)3.08 × 10²⁷ kg

Question 49

A satellite of mass M takes time T to orbit a planet.If the satellite had twice as much mass,the time for it to orbit the planet at the same altitude would be

A)4T.
B)2T.
C)T.
D)T/2.
E)T/4.

Question 50

You are the science officer on a visit to a distant solar system.Prior to landing on a planet you measure its diameter to be 1.8 × 10⁷ m.You have previously determined that the planet orbits 2.9 × 10¹¹ m from its star with a period of 402 earth days.Once on the surface you find that the acceleration due to gravity is 19.5 m/s².What are the masses of (a)the planet and (b)the star? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)(a)2.4 kg × kg,(b)1.2 kg ×
kg
B)(a)4.3 kg × kg,(b)1.2 kg ×
kg
C)(a)2.4 kg × kg,(b)7.1 kg ×
kg
D)(a)4.3 kg × kg,(b)7.1 kg ×
kg

Question 51

In another solar system,a planet has a moon that is 4.0 × 10⁵ m in diameter.Measurements reveal that this moon takes 3.0 x 10⁵ s to make each orbit of diameter 1.8 × 10⁸ m.What is the mass of the planet? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)1.2 × 10²⁴ kg
B)1.7 × 10²⁴ kg
C)2.4 × 10²⁴ kg
D)3.4 × 10²⁴ kg
E)4.8 × 10²⁴ kg

Question 52

Europa,a satellite of Jupiter,has an orbital diameter of 1.34 × 10⁹ m and a period of 3.55 days.What is the mass of Jupiter? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)1.53 × 10²⁷ kg
B)1.65 × 10²⁷ kg
C)1.07 × 10²⁷ kg
D)1.89 × 10²⁷ kg
E)3.08 × 10²⁷ kg

Question 53

The captain of a spaceship orbiting planet X discovers that to remain in orbit at
From the planet's center,she needs to maintain a speed of
What is the mass of planet X? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A)2.8 × 10¹⁹ kg
B)4.2 × 10¹⁷ kg
C)2.8 × 10¹⁶ kg
D)4.2 × 10¹⁴ kg