Question 1

State Kepler's third law of planetary motion.

Accepted Answer

The ratio of the squares of the periods of any two planets revolving about the Sun is equal to the ratio of the cubes of their semimajor axes.

Question 2

Jupiter completes one revolution about its own axis every 9.92 hours. What is the radius of the orbit required for a satellite to revolve about Jupiter with the same period? Jupiter has a mass of 1.90 × 1027 kg and G = 6.67 x 10-11 N•m2/kg2.

Accepted Answer

A) 1.04 × 107 m 
B) 2.26 × 109 m 
C) 1.60 × 108 m 
D) 3.41 × 108 m 
E) 7.45 × 108 m 
A) 1.04 × 107 m 
B) 2.26 × 109 m 
C) 1.60 × 108 m 
D) 3.41 × 108 m 
E) 7.45 × 108 m C

Question 3

A thin uniform spherical shell exerts a force on a particle located outside of it as if all the shell's mass were located at the center.

Accepted Answer

A) True 
 B)False  True

Question 4

A spherical shell of inner diameter R and outer diameter 3R has a uniform density ρ. What is the magnitude of the gravitational acceleration a distance 2R from the center of the spherical shell?

Accepted Answer

A) 15πGρR/7 
B) 32πGρR/5 
C) 25πGρR/12 
D) 7πGρR/6 
E) 7πGρR/3 
A) 15πGρR/7 
B) 32πGρR/5 
C) 25πGρR/12 
D) 7πGρR/6 
E) 7πGρR/3

Question 5

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 107 m. The second planet has an orbital radius 3.00 × 107 m. What is the period of the second satellite?

Accepted Answer

A) 60.8 hours 
B) 12.0 hours 
C) 33.1 hours 
D) 9.80 hours 
E) 27.0 hours 
A) 60.8 hours 
B) 12.0 hours 
C) 33.1 hours 
D) 9.80 hours 
E) 27.0 hours

Question 6

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 on the surface of Earth, the acceleration due to gravity on the surface of Z-34 is

Accepted Answer

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

Question 7

Apparent weightlessness can be experienced in freely falling elevator.

Accepted Answer

A) True 
 B)False

Question 8

A satellite orbits just above the Earth's surface. (a) Calculate the period of the satellite. (b) Calculate the speed of the satellite.

Accepted Answer

(a) 5040 s

Question 9

Uranus completes one revolution about its own axis every 17.24 hours. What is the radius of the orbit required for a satellite to revolve about Uranus with the same period? Uranus has a mass of 8.69 × 1025 kg and G = 6.67 x 10-11 N•m2/kg2.

Accepted Answer

A) 8.27 × 107 m 
B) 3.41 × 108 m 
C) 2.56 × 108 m 
D) 9.03 × 107 m 
E) 1.04 × 107 m 
A) 8.27 × 107 m 
B) 3.41 × 108 m 
C) 2.56 × 108 m 
D) 9.03 × 107 m 
E) 1.04 × 107 m

Question 10

Sputnik I was launched into orbit around Earth in 1957. It had a perigee (the closest approach to Earth, measured from Earth's center) of 6.81 × 106 m and an apogee (the furthest point from Earth's center) of 7.53 × 106 m. What was its speed when it was at its perigee? The mass of Earth is 5.97 × 1024 kg and
G = 6.67 x 10-11 N•m2/kg2.

Accepted Answer

A) 7.18 × 103 m/s 
B) 7.84 × 103 m/s 
C) 8.23 × 103 m/s 
D) 11.0 × 103 m/s 
E) 13.4 × 103 m/s 
A) 7.18 × 103 m/s 
B) 7.84 × 103 m/s 
C) 8.23 × 103 m/s 
D) 11.0 × 103 m/s 
E) 13.4 × 103 m/s

Question 11

The acceleration of gravity can vary locally on the Earth's surface because of the presence of rocks of different densities.

Accepted Answer

A) True 
 B)False

Question 12

During a lunar eclipse, the Moon, Earth, and Sun all lie on the same line, with the Earth between the Moon and the Sun. The Moon has a mass of 7.36 × 1022 kg; the Earth has a mass of 5.98 × 1024 kg; and the Sun has a mass of 1.99 × 1030 kg. The separation between the Moon and the Earth is given by 3.84 × 108 m; the separation between the Earth and the Sun is given by 1.496 × 1011 m.
(a) Calculate the force exerted on the Earth by the Moon.
(b) Calculate the force exerted on the Earth by the Sun.
(c) Calculate the net force exerted on the Earth by the Moon and the Sun.

Accepted Answer

(a) 1.99 × 10²⁰ N, tow

Question 13

A 2.00 × 108-kg mass is located at x = 100 m, y = 0.00 m. A 5.00 × 108-kg mass is located at x = 0.00 m, y = 200 m. Determine the gravitational force on a 3.00-kg mass located at x = 0.00 m, y = 0.00 m.

Accepted Answer

A) 4.00 × 10-4 N   - 5.00 × 10-4 N
  
B) 4.00 × 10-4 N   + 5.00 × 10-4 N
  
C) -4.00 × 10-4 N   + 5.00 × 10-4 N
  
D) 4.00 × 10-6 N   - 2.50 × 10-6 N
  
E) 4.00 × 10-6 N   + 2.50 × 10-6 N
  
A) 4.00 × 10-4 N   - 5.00 × 10-4 N
  
B) 4.00 × 10-4 N   + 5.00 × 10-4 N
  
C) -4.00 × 10-4 N   + 5.00 × 10-4 N
  
D) 4.00 × 10-6 N   - 2.50 × 10-6 N
  
E) 4.00 × 10-6 N   + 2.50 × 10-6 N

Question 14

List the fundamental forces in nature.

Accepted Answer

gravitational force,

Question 15

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 107 m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

Accepted Answer

A) 4.50 × 107 m 
B) 3.90 × 107 m 
C) 9.24 × 107 m 
D) 8.00 × 107 m 
E) 7.27 × 107 m 
A) 4.50 × 107 m 
B) 3.90 × 107 m 
C) 9.24 × 107 m 
D) 8.00 × 107 m 
E) 7.27 × 107 m

Question 16

The gravitational force that the Sun exerts on Earth is much larger than the gravitational force that Earth exerts on the Sun.

Accepted Answer

A) True 
 B)False

Question 17

The mass of the Moon is 7.4 × 1022 kg and its mean radius is 1.75 × 103 km. What is the acceleration due to gravity at the surface of the Moon?

Accepted Answer

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  
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 18

Two massive objects are fixed in position. A third object is placed directly between the first two at the position at which the total gravitational force on the third object due to the two massive objects is zero. The object is displaced slightly toward one of the two massive objects, the total gravitational force on the third object is now

Accepted Answer

A) zero. 
B) in a direction which depends on which of the massive objects has a greater mass. 
C) in the same direction the object is displaced. 
D) in the opposite direction to the displacement of the object. 
E) perpendicular to the displacement of the object. 
A) zero. 
B) in a direction which depends on which of the massive objects has a greater mass. 
C) in the same direction the object is displaced. 
D) in the opposite direction to the displacement of the object. 
E) perpendicular to the displacement of the object.

Question 19

You have discovered a new asteroid, which has a moon in an elliptical orbit around it. From a series of observations, you establish that the closest approach occurs when the moon is 49,000 m from the asteroid, the furthest separation is 98,000 m, and the speed of the moon at the point of closest approach is 7.50 m/s. What is the mass of the asteroid? G = 6.67 x 10-11 N•m2/kg2.

Accepted Answer

A) 4.25 × 1016 kg 
B) 9.87 × 1016 kg 
C) 3.10 × 1016 kg 
D) 2.04 × 1016 kg 
E) 5.05 × 1016 kg 
A) 4.25 × 1016 kg 
B) 9.87 × 1016 kg 
C) 3.10 × 1016 kg 
D) 2.04 × 1016 kg 
E) 5.05 × 1016 kg

Question 20

The gravitational force exerted on a particle outside a sphere with a spherically symmetric mass distribution is the same as if the entire mass of the sphere was concentrated at its center.

Accepted Answer

A) True 
 B)False

Exam 6: Gravitation and Newtons6 Synthesis

State Kepler's third law of planetary motion.

Jupiter completes one revolution about its own axis every 9.92 hours. What is the radius of the orbit required for a satellite to revolve about Jupiter with the same period? Jupiter has a mass of 1.90 × 1027 kg and G = 6.67 x 10-11 N•m2/kg2.

A thin uniform spherical shell exerts a force on a particle located outside of it as if all the shell's mass were located at the center.

A spherical shell of inner diameter R and outer diameter 3R has a uniform density ρ. What is the magnitude of the gravitational acceleration a distance 2R from the center of the spherical shell?

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 107 m. The second planet has an orbital radius 3.00 × 107 m. What is the period of the second satellite?

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 on the surface of Earth, the acceleration due to gravity on the surface of Z-34 is

Apparent weightlessness can be experienced in freely falling elevator.

A satellite orbits just above the Earth's surface. (a) Calculate the period of the satellite. (b) Calculate the speed of the satellite.

Uranus completes one revolution about its own axis every 17.24 hours. What is the radius of the orbit required for a satellite to revolve about Uranus with the same period? Uranus has a mass of 8.69 × 1025 kg and G = 6.67 x 10-11 N•m2/kg2.

The acceleration of gravity can vary locally on the Earth's surface because of the presence of rocks of different densities.

A 2.00 × 108-kg mass is located at x = 100 m, y = 0.00 m. A 5.00 × 108-kg mass is located at x = 0.00 m, y = 200 m. Determine the gravitational force on a 3.00-kg mass located at x = 0.00 m, y = 0.00 m.

List the fundamental forces in nature.

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 107 m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

The gravitational force that the Sun exerts on Earth is much larger than the gravitational force that Earth exerts on the Sun.

The mass of the Moon is 7.4 × 1022 kg and its mean radius is 1.75 × 103 km. What is the acceleration due to gravity at the surface of the Moon?

The gravitational force exerted on a particle outside a sphere with a spherically symmetric mass distribution is the same as if the entire mass of the sphere was concentrated at its center.

Introduction, Measurement, Estimating

Describing Motion: Kinematics in One Dimension

Kinematics in Two or Three Dimensions; Vectors

Dynamics: Newtons Laws of Motion

Using Newtons Laws: Friction, Circular Motion, Drag Forces

Work and Energy

Conservation of Energy

Linear Momentum

Rotational Motion

Angular Momentum; General Rotation

Static Equilibrium; Elasticity and Fracture

Fluids

Oscillations

Wave Motion

Sound

Temperature, Thermal Expansion, and the Ideal Gas Law

Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

Second Law of Thermodynamics

Electric Charge and Electric Field

Gausss Law

Electric Potential

Capacitance, Dielectrics, Electric Energy Storage

Electric Currents and Resistance

Dc Circuits

Magnetism

Sources of Magnetic Field

Electromagnetic Induction and Faradays Law

Inductance, Electromagnetic Oscillations, and Ac Circuits

Maxwells Equations and Electromagnetic Waves

Light: Reflection and Refraction

Lenses and Optical Instruments

The Wave Nature of Light; Interference

Diffraction and Polarization

Special Theory of Relativity

Early Quantum Theory and Models of the Atom

Quantum Mechanics

Quantum Mechanics of Atoms

Molecules and Solids

Nuclear Physics and Radioactivity

Nuclear Energy: Efects and Uses of Radiation

Elementary Particle

Astrophysics and Cosmology

Filters

Jupiter completes one revolution about its own axis every 9.92 hours. What is the radius of the orbit required for a satellite to revolve about Jupiter with the same period? Jupiter has a mass of 1.90 × 10²⁷ kg and G = 6.67 x 10^-11 N•m²/kg².

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 10⁷ m. The second planet has an orbital radius 3.00 × 10⁷ m. What is the period of the second satellite?

Uranus completes one revolution about its own axis every 17.24 hours. What is the radius of the orbit required for a satellite to revolve about Uranus with the same period? Uranus has a mass of 8.69 × 10²⁵ kg and G = 6.67 x 10^-11 N•m²/kg².

A 2.00 × 10⁸-kg mass is located at x = 100 m, y = 0.00 m. A 5.00 × 10⁸-kg mass is located at x = 0.00 m, y = 200 m. Determine the gravitational force on a 3.00-kg mass located at x = 0.00 m, y = 0.00 m.

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 10⁷ m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

The mass of the Moon is 7.4 × 10²² kg and its mean radius is 1.75 × 10³ km. What is the acceleration due to gravity at the surface of the Moon?