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American System Physics

A Physics Toolkit

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Representing Motion

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Accelerated Motion

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Forces in One Dimension

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Displacement and Force in Two Dimensions

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Motion in Two Dimensions

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Gravitation

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Rotational Motion

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Momentum and Its Conservation

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Energy and Its Conservation

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Thermal Energy

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States of Matter

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Vibrations and Waves

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Sound

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Fundamentals of Light

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Reflection and Refraction

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Interference and Diffraction

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Electrostatics

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Electric Current and Circuits

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Magnetic Fields

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Electromagnetic Induction and Electromagnetism

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Quantum Theory and the Atom

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Solid-State Electronics

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Nuclear and Particle Physics

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Quiz

7.2 Using the Law of Universal Gravitation – Quiz

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Using the Law of Universal Gravitation American Physics quiz: free practice for American System Physics. Work through this Using the Law of Universal Gravitation American Physics quiz and get instant feedback on every answer. If you get stuck, review the 7.2 Using the Law of Universal Gravitation — Notes lesson. More practice: American System Physics — all units. Syllabus: OpenStax free science textbooks.

  • Questions count: 50
  • Passing grade: A-
  • Time limit:
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1.
Diagrams A–D show proposed force diagrams for a satellite in a circular orbit around Earth (ignore air resistance). Which one is correct?
Dr Dabour Hub Academy - figure 1
A
B
D
C
2.
The diagram shows field lines around a planet with points X and Y at the distances marked. Which statement about the field is correct?
Dr Dabour Hub Academy - figure 2
The lines are closer together at X, and g at X is 4 times g at Y
The lines are closer together at X, and g at X is 2 times g at Y
The field is the same at X and Y because both lie on field lines
The lines point outward, so a mass at Y is pushed away from the planet
3.
Using the graph, at approximately what altitude is g about one ninth of its surface value?
Dr Dabour Hub Academy - figure 3
About 6 400 km
About 19 100 km
About 12 700 km
About 57 000 km
4.
In the diagram, projectiles are fired horizontally from a very high mountain at different speeds (air resistance ignored). Which labelled path is followed by a projectile fired at exactly the circular orbital speed?
Dr Dabour Hub Academy - figure 4
P
Q
R
S
5.
A satellite must photograph every part of Earth's surface over a few days. Which orbit in the diagram is suitable, and why?
Dr Dabour Hub Academy - figure 5
Orbit 1, because a low polar orbit passes over all latitudes as Earth rotates beneath it
Orbit 2, because it stays above one point on the equator
Orbit 2, because a larger orbit gives a faster satellite
Orbit 1, because its period is exactly 24 h
6.
Satellite A orbits at 1.5R. Using the orbital radii shown in the diagram, how do the orbital speeds of satellites A and B compare?
Dr Dabour Hub Academy - figure 6
vA = 9 × vB
vB = 3 × vA
vA = 81 × vB
vA = 3 × vB
7.
An astronaut measures the same bag on the Moon with a beam balance and a spring balance (diagram). What do the measurements give for the bag's mass and the Moon's gravitational field strength?
Dr Dabour Hub Academy - figure 7
Mass 3.2 kg; g = 1.6 N/kg
Mass 0.33 kg; g = 9.8 N/kg
Mass 2.0 kg; g = 3.2 N/kg
Mass 2.0 kg; g = 1.6 N/kg
8.
The bar chart shows the gravitational force on a 70 kg astronaut at different altitudes. At the 400 km altitude of a space station, what does the chart show?
Dr Dabour Hub Academy - figure 8
The force is zero, which is why astronauts float
The force is about 11% of its surface value
The force is still about 89% of its surface value, so gravity has not disappeared
The force is larger than at the surface because the astronaut is moving fast
9.
The graph shows the speed needed for circular orbits around Earth. Using the graph, what orbital speed is needed at a radius of 2.0 × 10⁷ m?
Dr Dabour Hub Academy - figure 9
About 8.9 km/s
About 4.5 km/s
About 2.2 km/s
About 7.7 km/s
10.
The table shows orbital radii and periods of Earth satellites, with the period of Sat 4 missing. Using Kepler's third law and the data in the table, what is the missing period?
6.58 h
12.0 h
21.9 h
4.41 h
11.
Students find the inertial mass of three trolleys (from m = F/a on an air track) and their gravitational mass (from weight on a balance). Which conclusion do the results in the table support?
Inertial mass is always larger than gravitational mass
Gravitational mass depends on the force applied
The two masses are unrelated
Inertial and gravitational mass are equal within experimental uncertainty
12.
Using the space-station data in the table, what is its orbital speed?
1.22 km/s
0.463 km/s
7.66 km/s
460 km/s
13.
A probe measures g at several distances from a planet's centre (table). To show that g follows an inverse-square law, which graph should be plotted to give a straight line through the origin?
g against r
g against r²
g against 1/r
g against 1/r²
14.
Using the data in the table for a satellite in a circular orbit, what centripetal force does gravity supply?
0.878 N
6530 N
4.70 × 10¹⁰ N
8330 N
15.
A weather agency needs continuous images of the same continent all day. Using the table, which orbit should its satellite use?
Low Earth orbit
Geostationary
Polar orbit
Any orbit with period under 2 h
16.
The table lists altitudes and recorded orbital speeds of four circular-orbit satellites. Checking with v = √(GmE/r), which recorded speed is wrong?
The satellite at 2,000 km
The satellite at 400 km
The satellite at 1,000 km
The satellite at 5,000 km
17.
An astronaut hangs known masses from a spring balance on the Moon and records the readings (table). What value of the Moon's gravitational field strength do the data give?
9.8 N/kg
0.62 N/kg
1.6 N/kg
3.2 N/kg
18.
A 500 kg satellite orbits 1500 km above Earth's surface. What is the gravitational force Earth exerts on it? (mE = 5.97 × 10²⁴ kg, RE = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)
3210 N
88,500 N
4900 N
2.53 × 10¹⁰ N
19.
What orbital speed does a satellite need for a circular orbit 400 km above Earth's surface? (mE = 5.97 × 10²⁴ kg, RE = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)
31.6 km/s
7.67 km/s
10.8 km/s
0.0588 km/s
20.
Earth has mass 5.97 × 10²⁴ kg and radius 6.37 × 10⁶ m. What is the gravitational field strength at an altitude of 200 km above its surface? (G = 6.67 × 10⁻¹¹ N·m²/kg²)
9950 N/kg
9.23 N/kg
9.81 N/kg
60.6 N/kg
21.
An Earth-observation craft travels on a circular path at an altitude of 300 km. How long does it take to complete one orbit? (mE = 5.97 × 10²⁴ kg, RE = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)
0.862 min
14.4 min
90.4 min
3.50 min
22.
A satellite orbits 400 km above Earth at 7.67 km/s. A second satellite with twice the mass is placed in the same orbit. What speed does it need?
15.3 km/s
7.67 km/s
5.42 km/s
3.84 km/s
23.
A student lists four equations used in orbit problems. Which pairing of equation and what it calculates is correct?
T = 2πr/v – the gravitational field strength
g = Gm/r² – the orbital period
v = √(Gm/r) – the speed for a circular orbit
W = mg – the mass of the object
24.
Satellite operators choose an orbit to suit the job. Which pairing of orbit type and typical use is correct?
Polar – fixed TV dish pointing
Geostationary – communications and TV
Low Earth orbit – 24 h period
Geostationary – scanning the whole Earth each day
25.
Units must be quoted with every answer in gravitation problems. Which pairing of quantity and its SI unit is correct?
Weight – kg
Mass – N
Gravitational field strength – N/kg
Orbital period – rad/s
26.
Which of these is a prediction of Einstein's general relativity, in which mass curves space-time?
Heavier objects fall faster than lighter ones
Gravity becomes repulsive at large distances
Light from a distant star is bent as it passes close to the Sun
Satellites need a forward force to stay in orbit
27.
Mass and weight are often confused in everyday speech. Which pairing of quantity and correct property is right?
Mass – a vector pointing down
Weight – measured in kilograms
Mass – becomes smaller on the Moon
Weight – measured with a newton meter
28.
A moon moves in a circular orbit of radius 6.71 × 10⁸ m with a period of 3.07 × 10⁵ s. What is the mass of the body it orbits? (G = 6.67 × 10⁻¹¹ N·m²/kg²)
1.90 × 10²⁷ kg
4.81 × 10²⁵ kg
2.83 × 10¹⁸ kg
5.83 × 10³² kg
29.
The Moon orbits Earth at a radius of 3.84 × 10⁸ m with a period of 27.3 days. What is its orbital speed?
1020 m/s
163 m/s
8.84 × 10⁷ m/s
6430 m/s
30.
When GMm/r² is set equal to mv²/r for a satellite, the satellite's mass m _____, so its speed does not depend on it.
cancels
doubles
becomes the central mass
increases the speed
31.
Einstein's theory describing gravity as the curving of space-time by mass is called general _____.
gravitation
relativity
mechanics
inertia
32.
A spring balance (newton meter) measures _____, whereas a beam balance compares masses.
weight
mass
density
inertia
33.
The speed a satellite needs for a circular orbit of radius r around mass M is v = _____.
√(2GM/r)
√(GM/r)
GM/r²
√(GMr)
34.
At an altitude of one Earth radius, g is about _____ N/kg.
4.9
9.8
1.09
2.45
35.
A projectile fired horizontally from a mountain at less than orbital speed eventually falls back to Earth. True or false?
True
False
False, because any horizontal speed leads to orbit
True only when it is fired at night
36.
Astronauts on the International Space Station feel weightless because there is no gravity at that altitude. True or false?
False, because g there is still about 90% of its surface value; they feel weightless because they are in free fall with the station
True
True only when the station is in a geostationary orbit
False, because the station is outside Earth's atmosphere
37.
Weight is a scalar quantity measured in kilograms. True or false?
True
True only when the object is on the Moon
False, because weight is a vector measured in kilograms
False, because weight is a force – a vector measured in newtons, directed towards the planet's centre
38.
At a distance of two Earth radii from Earth's centre, the gravitational field strength is about 2.45 N/kg. True or false?
False
False, because g is about 4.9 N/kg there
True only when the object is stationary
True
39.
A geostationary satellite could be positioned permanently above a city far from the equator, such as London. True or false?
True
True only when the satellite's speed is increased
False, because geostationary satellites orbit the poles
False, because a geostationary orbit must lie in the equatorial plane, so it can only stay above points on the equator
40.
A heavier satellite must travel faster than a lighter one to stay in the same circular orbit. True or false?
True
True only when the orbit is geostationary
False, because orbital speed v = √(GM/r) does not depend on the satellite's mass
False, because heavier satellites need to travel more slowly
41.
A student timing ten orbits of a simulated satellite and dividing by ten reduces the percentage uncertainty in the period compared with timing one orbit. True or false?
True
False
False, because repeating makes the reaction-time error larger
True only when the orbit is circular
42.
A satellite moving in a circular orbit at constant speed is accelerating. True or false?
False
True
False, because constant speed means zero acceleration
True only when it is in a polar orbit
43.
A satellite in low Earth orbit at about 300 km altitude takes roughly 90 minutes to go round once. True or false?
False
True
False, because it takes about 24 hours
True only when it is geostationary
44.
Astronauts on a space station 400 km up experience only about 10% of the gravitational field strength at Earth's surface. True or false?
True
True only when the station is in shadow
False, because they experience about 90% of surface g; they feel weightless because they are in free fall
False, because they experience 0% of surface g
45.
Inertial mass and gravitational mass have been found experimentally to be equal. True or false?
False
False, because inertial mass is always twice gravitational mass
True only when the object is at rest
True
46.
A beam balance gives the same reading for an object on the Moon as on Earth. True or false?
True
False
False, because the reading is one sixth as large on the Moon
True only when the Moon is full
47.
Satellites in lower orbits around Earth move faster than satellites in higher orbits. True or false?
False
False, because all Earth satellites have the same speed
True only when they have larger masses
True
48.
A geostationary satellite orbits above the equator with a period of 24 h in the same direction as Earth rotates. True or false?
False
True
False, because it orbits over the poles
True only when it is in low Earth orbit
49.
For a satellite in a circular orbit, gravity is the only force acting and it provides the centripetal force. True or false?
False
False, because a forward thrust force is needed to keep it moving
True
True only when the satellite has rocket engines firing
50.
If a satellite's orbital radius is doubled, its orbital speed also doubles. True or false?
True
True only when the satellite's mass also doubles
False, because v ∝ 1/√r, so doubling r reduces v by a factor of √2
False, because the speed is halved
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