Question 1

A baseball is located at the surface of the earth.Which statements about it are correct? (There may be more than one correct choice.)

Accepted Answer

A)  The earth exerts a much greater gravitational force on the ball than the ball exerts on the earth. 
B)  The ball exerts a greater gravitational force on the earth than the earth exerts on the ball. 
C)  The gravitational force on the ball due to the earth is exactly the same as the gravitational force on the earth due to the ball. 
D)  The gravitational force on the ball is independent of the mass of the ball. 
E)  The gravitational force on the ball is independent of the mass of the earth. 
A)  The earth exerts a much greater gravitational force on the ball than the ball exerts on the earth. 
B)  The ball exerts a greater gravitational force on the earth than the earth exerts on the ball. 
C)  The gravitational force on the ball due to the earth is exactly the same as the gravitational force on the earth due to the ball. 
D)  The gravitational force on the ball is independent of the mass of the ball. 
E)  The gravitational force on the ball is independent of the mass of the earth. C

Question 2

A certain spherical asteroid has a mass of 3.5 × 1016 kg and a radius of 8.8 km.What is the minimum speed needed to escape from the surface of this asteroid? (G = 6.67 × 10-11 N • m2/kg2)

Accepted Answer

A)  23 m/s 
B)  16 m/s 
C)  520 m/s 
D)  730 m/s 
A)  23 m/s 
B)  16 m/s 
C)  520 m/s 
D)  730 m/s A

Question 3

A small planet having a radius of 1000 km exerts a gravitational force of 100 N on an object that is 500 km above its surface.If this object is moved 500 km farther from the planet,the gravitational force on it will be closest to

Accepted Answer

A)  75 N. 
B)  71 N. 
C)  56 N. 
D)  50 N. 
E)  25 N. 
A)  75 N. 
B)  71 N. 
C)  56 N. 
D)  50 N. 
E)  25 N. C

Question 4

The moons of Mars,Phobos (Fear)and Deimos (Terror),are very close to the planet compared to Earth's Moon.Their orbital radii are 9,378 km and 23,459 km respectively.What is the ratio of the orbital speed of Phobos to that of Deimos?

Accepted Answer

A)  0.2528 
B)  0.3998 
C)  1.582 
D)  2.858 
E)  3.956 
A)  0.2528 
B)  0.3998 
C)  1.582 
D)  2.858 
E)  3.956

Question 5

A satellite is orbiting the earth.If a payload of material is added until it doubles the satellite's mass,the earth's pull of gravity on this satellite will double but the satellite's orbit will not be affected.

Accepted Answer

A) True 
 B)False

Question 6

Three identical very small 50-kg masses are held at the corners of an equilateral triangle,0.30 m on each side.If one of the masses is released,what is 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)

Accepted Answer

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 
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 7

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 and its rotation period to be 22.3 hours.You have previously determined that the planet orbits 1.8 × 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 59.7 m/s2.What are the mass of (a)the planet and (b)the star? (G = 6.67 × 10-11 N • m2/kg2.)

Accepted Answer

A)  (a) 7.2 kg × 1025 kg, (b) 2.9 kg × 1030 kg 
B)  (a) 1.3 kg × 1026 kg, (b) 2.9 kg × 1030 kg 
C)  (a) 7.2 kg × 1025 kg, (b) 1.7 kg × 1030 kg 
D)  (a) 1.3 kg × 1026 kg, (b) 1.7 kg × 1030 kg 
A)  (a) 7.2 kg × 1025 kg, (b) 2.9 kg × 1030 kg 
B)  (a) 1.3 kg × 1026 kg, (b) 2.9 kg × 1030 kg 
C)  (a) 7.2 kg × 1025 kg, (b) 1.7 kg × 1030 kg 
D)  (a) 1.3 kg × 1026 kg, (b) 1.7 kg × 1030 kg

Question 8

Suppose we want a satellite to revolve around the earth 5 times a day.What should be the radius of its orbit? (The mass of the earth is 5.97 × 1024 kg,G = 6.67 × 10-11 N • m2/kg2,and you can neglect the presence of the moon.)

Accepted Answer

A)  1.44 × 107 m 
B)  0.690 × 107 m 
C)  7.22 × 107 m 
D)  2.11 × 107 m 
A)  1.44 × 107 m 
B)  0.690 × 107 m 
C)  7.22 × 107 m 
D)  2.11 × 107 m

Question 9

A satellite of mass m has an orbital period T when it is in a circular orbit of radius R around the earth.If the satellite instead had mass 4m,its orbital period would be

Accepted Answer

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

Question 10

The International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is 5.97 × 1024 kg,the radius of the earth is 6.38 × 106 m,and
G = 6.67 × 10-11 N • m2/kg2.Assuming a circular orbit,
(a)what is the period of the International Space Station's orbit?
(b)what is the speed of the International Space Station in its orbit?

Accepted Answer

(a)5.52 ×

Question 11

By how many newtons does the weight of a 100-kg person change when he goes from sea level to an altitude of 5.0 km if we neglect the earth's rotational effects? (The mean radius of the Earth is 6.38 × 106 m,G = 6.67 × 10-11 N • m2/kg2.)

Accepted Answer

A)  -0.60 N 
B)  -1.5 N 
C)  -2.6 N 
D)  -3.6 N 
E)  -5.2 N 
A)  -0.60 N 
B)  -1.5 N 
C)  -2.6 N 
D)  -3.6 N 
E)  -5.2 N

Question 12

An astronaut is in equilibrium when he is positioned 140 km from the center of asteroid X and 581 km from the center of asteroid Y,along the straight line joining the centers of the asteroids.What is the ratio of the masses X/Y of the asteroids?

Accepted Answer

A)  0.0581 
B)  17.2 
C)  0.241 
D)  4.15 
A)  0.0581 
B)  17.2 
C)  0.241 
D)  4.15

Question 13

A very small round ball is located near a large solid sphere of uniform density.The force that the large sphere exerts on the ball

Accepted Answer

A)  is exactly the same as it would be if all the mass of the sphere were concentrated at the center of the sphere. 
B)  is approximately the same as it would be if all the mass of the sphere were concentrated at the center of the sphere. 
C)  is independent of the mass of the ball. 
D)  is independent of the mass of the sphere. 
E)  can only be calculated using calculus. 
A)  is exactly the same as it would be if all the mass of the sphere were concentrated at the center of the sphere. 
B)  is approximately the same as it would be if all the mass of the sphere were concentrated at the center of the sphere. 
C)  is independent of the mass of the ball. 
D)  is independent of the mass of the sphere. 
E)  can only be calculated using calculus.

Question 14

A 910-kg object is released from rest at an altitude of 1200 km above the north pole of the earth.If we ignore atmospheric friction,with what speed does the object strike the surface of the earth?
(G = 6.67 × 10-11 N • m2/kg2,Mearth = 5.97 × 1024 kg,the polar radius of the earth is 6357 km)

Accepted Answer

A)  4.5 km/s 
B)  2.2 km/s 
C)  2.7 km/s 
D)  3.2 km/s 
E)  4.8 km/s 
A)  4.5 km/s 
B)  2.2 km/s 
C)  2.7 km/s 
D)  3.2 km/s 
E)  4.8 km/s

Question 15

What is the period (in hours)of a satellite circling Mars 100 km above the planet's surface? The mass of Mars is 6.42 × 1023 kg,its radius is 3.40 × 106 m,and G = 6.67 × 10-11 N • m2/kg2.

Accepted Answer

A)  1.75 h 
B)  1.25 h 
C)  1.15 h 
D)  1.00 h 
E)  1.45 h 
A)  1.75 h 
B)  1.25 h 
C)  1.15 h 
D)  1.00 h 
E)  1.45 h

Question 16

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

Question 17

Two planets having equal masses are in circular orbit around a star.Planet A has a smaller orbital radius than planet B.Which statement is true?

Accepted Answer

A)  Planet A has more kinetic energy, less potential energy, and less mechanical energy (potential plus kinetic) than planet B. 
B)  Planet A has more kinetic energy, more potential energy, and more mechanical energy (potential plus kinetic) than planet B. 
C)  Planet A has more kinetic energy, less potential energy, and more mechanical energy (potential plus kinetic) than planet B. 
D)  Planet A and planet B have the same amount of mechanical energy (potential plus kinetic). 
A)  Planet A has more kinetic energy, less potential energy, and less mechanical energy (potential plus kinetic) than planet B. 
B)  Planet A has more kinetic energy, more potential energy, and more mechanical energy (potential plus kinetic) than planet B. 
C)  Planet A has more kinetic energy, less potential energy, and more mechanical energy (potential plus kinetic) than planet B. 
D)  Planet A and planet B have the same amount of mechanical energy (potential plus kinetic).

Question 18

A huge cannon is assembled on an airless planet having insignificant axial spin.The planet has a radius of 5.00 × 106 m and a mass of 3.95 × 1023 kg.The cannon fires a projectile straight up at 2000 m/s. An observation satellite orbits the planet at a height of 1000 km.What is the projectile's speed as it passes the satellite? (G = 6.67 × 10-11 N • m2/kg2)

Accepted Answer

A)  1500 m/s 
B)  1380 m/s 
C)  1610 m/s 
D)  1280 m/s 
A)  1500 m/s 
B)  1380 m/s 
C)  1610 m/s 
D)  1280 m/s

Question 19

A satellite in a circular orbit of radius R around planet X has an orbital period T.If Planet X had one-fourth as much mass,the orbital period of this satellite in an orbit of the same radius would be

Accepted Answer

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

Question 20

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

Exam 13: Gravity

A baseball is located at the surface of the earth.Which statements about it are correct? (There may be more than one correct choice.)

A certain spherical asteroid has a mass of 3.5 × 1016 kg and a radius of 8.8 km.What is the minimum speed needed to escape from the surface of this asteroid? (G = 6.67 × 10-11 N • m2/kg2)

A small planet having a radius of 1000 km exerts a gravitational force of 100 N on an object that is 500 km above its surface.If this object is moved 500 km farther from the planet,the gravitational force on it will be closest to

The moons of Mars,Phobos (Fear)and Deimos (Terror),are very close to the planet compared to Earth's Moon.Their orbital radii are 9,378 km and 23,459 km respectively.What is the ratio of the orbital speed of Phobos to that of Deimos?

A satellite is orbiting the earth.If a payload of material is added until it doubles the satellite's mass,the earth's pull of gravity on this satellite will double but the satellite's orbit will not be affected.

Three identical very small 50-kg masses are held at the corners of an equilateral triangle,0.30 m on each side.If one of the masses is released,what is 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)

Suppose we want a satellite to revolve around the earth 5 times a day.What should be the radius of its orbit? (The mass of the earth is 5.97 × 1024 kg,G = 6.67 × 10-11 N • m2/kg2,and you can neglect the presence of the moon.)

A satellite of mass m has an orbital period T when it is in a circular orbit of radius R around the earth.If the satellite instead had mass 4m,its orbital period would be

By how many newtons does the weight of a 100-kg person change when he goes from sea level to an altitude of 5.0 km if we neglect the earth's rotational effects? (The mean radius of the Earth is 6.38 × 106 m,G = 6.67 × 10-11 N • m2/kg2.)

An astronaut is in equilibrium when he is positioned 140 km from the center of asteroid X and 581 km from the center of asteroid Y,along the straight line joining the centers of the asteroids.What is the ratio of the masses X/Y of the asteroids?

A very small round ball is located near a large solid sphere of uniform density.The force that the large sphere exerts on the ball

A 910-kg object is released from rest at an altitude of 1200 km above the north pole of the earth.If we ignore atmospheric friction,with what speed does the object strike the surface of the earth? (G = 6.67 × 10-11 N • m2/kg2,Mearth = 5.97 × 1024 kg,the polar radius of the earth is 6357 km)

What is the period (in hours)of a satellite circling Mars 100 km above the planet's surface? The mass of Mars is 6.42 × 1023 kg,its radius is 3.40 × 106 m,and G = 6.67 × 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?

Two planets having equal masses are in circular orbit around a star.Planet A has a smaller orbital radius than planet B.Which statement is true?

A satellite in a circular orbit of radius R around planet X has an orbital period T.If Planet X had one-fourth as much mass,the orbital period of this satellite in an orbit of the same radius would be

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?

Foundations

A: Foundations

Motion in One Dimension

Acceleration

Momentum

Energy

Principle of Relativity

Interactions

Force

Work

Motion in a Plane

Motion in a Circle

Torque

Special Relativity

Periodic Motion

Waves in One Dimension

Waves in Two and Three Dimensions

Fluids

Entropy

Energy Transferred Thermally

Degradation of Energy

Electric Interactions

The Electric Field

Gausss Law

Work and Energy in Electrostatics

Charge Separation and Storage

Magnetic Interactions

Magnetic Fields of Charged Particles in Motion

Changing Magnetic Fields

Changing Electric Fields

Electric Circuits

Electronics

Ray Optics

Wave and Particle Optics

Filters

A certain spherical asteroid has a mass of 3.5 × 10¹⁶ kg and a radius of 8.8 km.What is the minimum speed needed to escape from the surface of this asteroid? (G = 6.67 × 10^-11 N • m²/kg²)

Suppose we want a satellite to revolve around the earth 5 times a day.What should be the radius of its orbit? (The mass of the earth is 5.97 × 10²⁴ kg,G = 6.67 × 10^-11 N • m²/kg²,and you can neglect the presence of the moon.)

By how many newtons does the weight of a 100-kg person change when he goes from sea level to an altitude of 5.0 km if we neglect the earth's rotational effects? (The mean radius of the Earth is 6.38 × 10⁶ m,G = 6.67 × 10^-11 N • m²/kg².)

What is the period (in hours)of a satellite circling Mars 100 km above the planet's surface? The mass of Mars is 6.42 × 10²³ kg,its radius is 3.40 × 10⁶ m,and G = 6.67 × 10^-¹¹N • 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?

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?