Question 1

What is the escape speed from a planet of mass M and radius R if M = 3.2 × 1023 kg and R = 2.4 × 106 m?

Accepted Answer

A)  5.5 km/s 
B)  4.2 km/s 
C)  5.2 km/s 
D)  4.8 km/s 
E)  3.7 km/s 
A)  5.5 km/s 
B)  4.2 km/s 
C)  5.2 km/s 
D)  4.8 km/s 
E)  3.7 km/s

Question 2

The period of oscillation of a near-Earth satellite (neglecting atmospheric effects) is 84.3 min. What is the period of a near-Moon satellite? (RE = 6.37 × 106 m; RM = 1.74 × 106 m; ME = 5.98 × 1024 kg; MM = 7.36 × 1022 kg.)

Accepted Answer

A)  6.03 × 10−3 min. 
B)  0.713 min. 
C)  84.3 min. 
D)  108 min. 
E)  140 min. 
A)  6.03 × 10−3 min. 
B)  0.713 min. 
C)  84.3 min. 
D)  108 min. 
E)  140 min.

Question 3

An asteroid revolves around the Sun with a perihelion 0.5 AU and an aphelion of 7.5 AU. What is its period of revolution?

Accepted Answer

A)  4 years 
B)  8 years 
C)  16 years 
D)  32 years 
E)  64 years 
A)  4 years 
B)  8 years 
C)  16 years 
D)  32 years 
E)  64 years

Question 4

A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 × 106 m. What is the magnitude of the gravitational force on the satellite by planet Cruton?

Accepted Answer

A)  63 N 
B)  58 N 
C)  68 N 
D)  73 N 
E)  50 N 
A)  63 N 
B)  58 N 
C)  68 N 
D)  73 N 
E)  50 N

Question 5

In an isolated system of two bodies that exert gravitational forces on one another, the quantity (quantities) that remain(s) constant is(are)

Accepted Answer

A)  the total energy of the system. 
B)  the total angular momentum of the system. 
C)  the angular positions of the two bodies. 
D)  all of the above. 
E)  only (a) and (b) above. 
A)  the total energy of the system. 
B)  the total angular momentum of the system. 
C)  the angular positions of the two bodies. 
D)  all of the above. 
E)  only (a) and (b) above.

Question 6

Calculate the Earth's angular momentum in the approximation that treats the Earth's orbit around the sun as a circle. (MSun = 1.99 × 1030 kg; T = 3.156 × 107 s; ME = 5.98 × 1024 kg.)

Accepted Answer

Question 7

A projectile is launched from the surface of a planet (mass = M, radius = R). What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E) 
  
A) 
  
B) 
  
C) 
  
D) 
  
E)

Question 8

Two satellites are placed in geosynchronous orbits, orbits with a period of 24 hours, where each satellite hovers over a spot on the Earth's equator. Satellite B has three times the mass of satellite A. What is the relationship between the magnitudes of the gravitational forces of the Earth on the two satellites?

Accepted Answer

A)  FB =
  FA. 
B)  FB =
  FA. 
C)  FB = FA. 
D)  FB = 3FA. 
E)  FB = 9FA. 
A)  FB =
  FA. 
B)  FB =
  FA. 
C)  FB = FA. 
D)  FB = 3FA. 
E)  FB = 9FA.

Question 9

An object is released from rest when it is a height h above the surface of a planet of mass M and radius R. What is the speed of the object just before striking the surface of the planet? Neglect any air resistance. Let h = 4.0 × 106 m, R = 5.0 × 106 m, and M = 4.0 × 1024 kg.

Accepted Answer

A)  7.8 km/s 
B)  3.5 km/s 
C)  5.4 km/s 
D)  6.9 km/s 
E)  4.8 km/s 
A)  7.8 km/s 
B)  3.5 km/s 
C)  5.4 km/s 
D)  6.9 km/s 
E)  4.8 km/s

Question 10

What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 × 106 m around the Earth? (Mass of Earth = 6.0 × 1024 kg.)

Accepted Answer

A)  5.0 × 109 J 
B)  1.0 × 1010 J 
C)  1.5 × 1010 J 
D)  2.0 × 1010 J 
E)  2.5 × 109 J 
A)  5.0 × 109 J 
B)  1.0 × 1010 J 
C)  1.5 × 1010 J 
D)  2.0 × 1010 J 
E)  2.5 × 109 J

Question 11

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Accepted Answer

A)  its speed is constant. 
B)  its speed is increasing. 
C)  its speed is decreasing. 
D)  its speed is a maximum. 
E)  its speed is a minimum. 
A)  its speed is constant. 
B)  its speed is increasing. 
C)  its speed is decreasing. 
D)  its speed is a maximum. 
E)  its speed is a minimum.

Question 12

Planet Zero has a mass of 5.0 × 1023 kg and a radius of 2.0 × 106 m. A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s. What is the speed of the probe when it is 3.0 × 106 m from Zero's center?

Accepted Answer

A)  3.0 km/s 
B)  2.2 km/s 
C)  1.6 km/s 
D)  3.7 km/s 
E)  5.9 km/s 
A)  3.0 km/s 
B)  2.2 km/s 
C)  1.6 km/s 
D)  3.7 km/s 
E)  5.9 km/s

Question 13

A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R). What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible?

Accepted Answer

A)  GmM/(4R) 
B)  GmM/R 
C)  GmM/(2R) 
D)  GmM/(3R) 
E)  2GmM/(5R) 
A)  GmM/(4R) 
B)  GmM/R 
C)  GmM/(2R) 
D)  GmM/(3R) 
E)  2GmM/(5R)

Question 14

Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have

Accepted Answer

A)  the smaller period. 
B)  the greater period. 
C)  the smaller gravitational mass. 
D)  the larger gravitational mass. 
E)  the larger universal gravitational constant. 
A)  the smaller period. 
B)  the greater period. 
C)  the smaller gravitational mass. 
D)  the larger gravitational mass. 
E)  the larger universal gravitational constant.

Question 15

The figure below shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Accepted Answer

A)  its speed is constant. 
B)  its speed is increasing. 
C)  its speed is decreasing. 
D)  its speed is a maximum. 
E)  its speed is a minimum. 
A)  its speed is constant. 
B)  its speed is increasing. 
C)  its speed is decreasing. 
D)  its speed is a maximum. 
E)  its speed is a minimum.

Question 16

What is the period of revolution of a planet in circular orbit around a star of 4.0 solar masses if it is at a distance from the star equal to that of the Earth from the Sun?

Accepted Answer

The answer of What is the period of revolution of...

Question 17

What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth, where R is the radius of the Earth?

Accepted Answer

A)  4.8 m/s2 
B)  1.1 m/s2 
C)  3.3 m/s2 
D)  2.5 m/s2 
E)  6.5 m/s2 
A)  4.8 m/s2 
B)  1.1 m/s2 
C)  3.3 m/s2 
D)  2.5 m/s2 
E)  6.5 m/s2

Question 18

When a falling meteor is at a distance above the Earth's surface of 3 times the Earth's radius, what is its acceleration due to the Earth's gravity?

Accepted Answer

The answer of When a falling meteor is at a...

Question 19

Which of the following quantities is conserved for a planet orbiting a star in a circular orbit? Only the planet itself is to be taken as the system; the star is not included.

Accepted Answer

A)  Momentum and energy. 
B)  Energy and angular momentum. 
C)  Momentum and angular momentum. 
D)  Momentum, angular momentum and energy. 
E)  None of the above. 
A)  Momentum and energy. 
B)  Energy and angular momentum. 
C)  Momentum and angular momentum. 
D)  Momentum, angular momentum and energy. 
E)  None of the above.

Question 20

A 50-kg satellite circles the Earth in an orbit with a period of 120 min. What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 × 106 m, mass = 6.0 × 1024 kg)

Accepted Answer

A)  2.9 × 108 J 
B)  3.5 × 108 J 
C)  4.1 × 108 J 
D)  4.7 × 108 J 
E)  5.9 × 108 J 
A)  2.9 × 108 J 
B)  3.5 × 108 J 
C)  4.1 × 108 J 
D)  4.7 × 108 J 
E)  5.9 × 108 J

Exam 13: Universal Gravitation

What is the escape speed from a planet of mass M and radius R if M = 3.2 × 1023 kg and R = 2.4 × 106 m?

The period of oscillation of a near-Earth satellite (neglecting atmospheric effects) is 84.3 min. What is the period of a near-Moon satellite? (RE = 6.37 × 106 m; RM = 1.74 × 106 m; ME = 5.98 × 1024 kg; MM = 7.36 × 1022 kg.)

An asteroid revolves around the Sun with a perihelion 0.5 AU and an aphelion of 7.5 AU. What is its period of revolution?

A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 × 106 m. What is the magnitude of the gravitational force on the satellite by planet Cruton?

In an isolated system of two bodies that exert gravitational forces on one another, the quantity (quantities) that remain(s) constant is(are)

Calculate the Earth's angular momentum in the approximation that treats the Earth's orbit around the sun as a circle. (MSun = 1.99 × 1030 kg; T = 3.156 × 107 s; ME = 5.98 × 1024 kg.)

A projectile is launched from the surface of a planet (mass = M, radius = R). What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere.

An object is released from rest when it is a height h above the surface of a planet of mass M and radius R. What is the speed of the object just before striking the surface of the planet? Neglect any air resistance. Let h = 4.0 × 106 m, R = 5.0 × 106 m, and M = 4.0 × 1024 kg.

What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 × 106 m around the Earth? (Mass of Earth = 6.0 × 1024 kg.)

The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

Planet Zero has a mass of 5.0 × 1023 kg and a radius of 2.0 × 106 m. A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s. What is the speed of the probe when it is 3.0 × 106 m from Zero's center?

A spacecraft (mass = m) orbits a planet (mass = M) in a circular orbit (radius = R). What is the minimum energy required to send this spacecraft to a distant point in space where the gravitational force on the spacecraft by the planet is negligible?

Two identical planets orbit a star in concentric circular orbits in the star's equatorial plane. Of the two, the planet that is farther from the star must have

The figure below shows a planet traveling in a clockwise direction on an elliptical path around a star located at one focus of the ellipse. When the planet is at point A,

What is the period of revolution of a planet in circular orbit around a star of 4.0 solar masses if it is at a distance from the star equal to that of the Earth from the Sun?

What is the magnitude of the free-fall acceleration at a point that is a distance 2R above the surface of the Earth, where R is the radius of the Earth?

When a falling meteor is at a distance above the Earth's surface of 3 times the Earth's radius, what is its acceleration due to the Earth's gravity?

Which of the following quantities is conserved for a planet orbiting a star in a circular orbit? Only the planet itself is to be taken as the system; the star is not included.

A 50-kg satellite circles the Earth in an orbit with a period of 120 min. What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 × 106 m, mass = 6.0 × 1024 kg)

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The Laws of Motion

Circular Motion and Other Applications of Newtons Laws

Energy of a System

Conservation of Energy

Linear Momentum and Collisions

Rotation of a Rigid Object About a Fixed Axis

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The First Law of Thermodynamics

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Image Formation

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Introduction to Quantum Physics

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Filters

What is the escape speed from a planet of mass M and radius R if M = 3.2 × 10²³ kg and R = 2.4 × 10⁶ m?

The period of oscillation of a near-Earth satellite (neglecting atmospheric effects) is 84.3 min. What is the period of a near-Moon satellite? (R_E = 6.37 × 10⁶ m; R_M = 1.74 × 10⁶ m; M_E = 5.98 × 10²⁴ kg; M_M = 7.36 × 10²² kg.)

A 50-kg satellite circles planet Cruton every 5.6 h in an orbit with a radius of 12 × 10⁶ m. What is the magnitude of the gravitational force on the satellite by planet Cruton?

Calculate the Earth's angular momentum in the approximation that treats the Earth's orbit around the sun as a circle. (M_Sun = 1.99 × 10³⁰ kg; T = 3.156 × 10⁷ s; M_E = 5.98 × 10²⁴ kg.)

An object is released from rest when it is a height h above the surface of a planet of mass M and radius R. What is the speed of the object just before striking the surface of the planet? Neglect any air resistance. Let h = 4.0 × 10⁶ m, R = 5.0 × 10⁶ m, and M = 4.0 × 10²⁴ kg.

What is the kinetic energy of a 200-kg satellite as it follows a circular orbit of radius 8.0 × 10⁶ m around the Earth? (Mass of Earth = 6.0 × 10²⁴ kg.)

Planet Zero has a mass of 5.0 × 10²³ kg and a radius of 2.0 × 10⁶ m. A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s. What is the speed of the probe when it is 3.0 × 10⁶ m from Zero's center?

A 50-kg satellite circles the Earth in an orbit with a period of 120 min. What minimum energy is required to change the orbit to another circular orbit with a period of 180 min? (Earth: radius = 6.4 × 10⁶ m, mass = 6.0 × 10²⁴ kg)