Deck 11: Gravity

Question 1

If the mass of a satellite is doubled while the radius of its orbit remains constant,the speed of the satellite is

A)increased by a factor of 8.
B)increased by a factor of 2.
C)not changed.
D)reduced by a factor of 8.
E)reduced by a factor of 2.

Answer 1

not changed.

Question 2

What is the force of gravity between the proton and electron in a hydrogen atom,given that G = 6.67 $\times$ 10^-11 N·m²/kg²,mass of a proton = 1.67 $\times$ 10^-27 kg,mass of an electron = 9.1 $\times$ 10^-31 kg,and average radius of the electron's orbit in the hydrogen atom = 0.0529 nm?

A)1.9 $\times$ 10^-57 N
B)1.9 $\times$ 10^-54 N
C)3.6 $\times$ 10^-53 N
D)3.6 $\times$ 10^-47 N
E)3.6 $\times$ 10^-41 N

Answer 2

3.6 $\times$ 10^-47 N

Question 3

In a distant galaxy,a planet orbits its sun at a distance of 1.8 $\times$ 10¹² m with a period of 10⁸s.A second planet orbits the same sun at a distance of 9 v 10¹¹ m.What is the period of the second planet?

A)5 $\times$ 10⁷ s
B)2 $\times$ 10⁸ s
C)0.35 $\times$ 10⁸ s
D)2.8 $\times$ 10⁸ s
E)5 $\times$ 10⁸ s

Answer 3

0.35 $\times$ 10⁸ s

Question 4

Use the figure to the right to answer the next problem. The orbits of two planets orbiting a star are shown.The semimajor axis of planet A is twice that of planet B.
If the period of planet B is T_B,the period of planet A is

A)2T_B
B)
C)3T_B
D)
E)4T_B

Question 5

The acceleration due to gravity at the surface of Earth is g.The radius of Earth is R_E.The distance from the center of Earth to a point where the acceleration due to gravity is g/9 is

A)R_E
B)9R_E
C)R_E/3
D)3R_E
E)None of these is correct.

Question 6

Halley's comet returns to the vicinity of the sun (and Earth)about once every 76 years.Its last appearance was in 1986.What is the average distance from Halley's comet to the sun,given that the average distance from Earth to the sun is 1.50 $\times$ 10¹¹m?

A)6.4 $\times$ 10¹¹ m
B)1.8 $\times$ 10¹² m
C)2.7 $\times$ 10¹² m
D)1.1 $\times$ 10¹³ m
E)9.9 $\times$ 10¹³ m

Question 7

Of the five masses in orbit around the central mass,the one with the longest period of revolution is

A)1
B)2
C)3
D)4
E)5

Question 8

Use the figure to the right to answer the next problem. The orbits of two planets orbiting a star are shown.The semimajor axis of planet A is twice that of planet B.
The speed of planet A when it is at A is _____ the speed at A'.

A)less than
B)equal to
C)greater than
D)unable to tell
E)depends on the mass of the star

Question 9

Kepler's law of the harmonic (the period-distance relationship)is an example of

A)a linear function.
B)a power function.
C)an exponential function.
D)a polynomial function.
E)a sinusoidal function.

Question 10

Of the satellites shown revolving around Earth,the one with the greatest speed is

A)1
B)2
C)3
D)4
E)5

Question 11

Earth and Mars are 1.0 AU and 1.52 AU away from the Sun,respectively.Given that the period of Earth's orbit around the Sun is 1 yr,calculate the period of the orbit of Mars around the Sun.(1 AU = 150 $\times$ 10⁶ km)

A)1.5 yr
B)0.53 yr
C)0.28 yr
D)1.9 yr
E)3.5 yr

Question 12

Kepler's second law of planetary motion states that the radius vector from the sun to a planet sweeps out equal areas in equal times.This relationship is a consequence of which of the following conservation principles?

A)speed
B)linear momentum
C)angular momentum
D)mechanical energy
E)potential energy

Question 13

What is the difference in the force of gravity on a 1.0-kg mass at the bottom of the deepest ocean trench and that at the top of the highest mountain? Assume that g = 9.8 m/s² at sea level.The radius of Earth at sea level is 6.37 $\times$ 10⁶ m.The deepest trench is the Marianas Trench,south of Guam,which has a depth
D = 1.103 $\times$ 10⁴ m below sea level.The highest mountain is Everest in Nepal,which has a height of h = 8.847 $\times$ 10³ m above sea level.The difference is

A)0.061 N
B)0.0067 N
C)0.027 N
D)0.034 N
E)0.0062 N

Question 14

The radius of the orbit of Earth around the Sun is 150 $\times$ 10⁶ km.If the orbital periods for Earth and Venus are 365 and 225 days respectively,calculate the radius of orbit for Venus in astronomical units AU.

A)0.85 AU
B)0.62 AU
C)0.72 AU
D)1.4 AU
E)2.1 AU

Question 15

Which of the following statements is true?

A)There is no point in the universe where gravity is precisely zero.
B)It is possible to find a point in the universe where gravity from different astronomical objects cancels so it is precisely zero.
C)Gravity can give rise to a repulsive force.
D)Gravity is a nonconservative force.
E)None of the above is true.

Question 16

The moon has a period of 27.3 d and is an average distance from Earth of 3.84 $\times$ 10⁵km.A communications satellite is placed in an Earth orbit at 4.23 $\times$ 10⁴ km from the center of Earth.What is the period of this satellite?

A)0.87 h
B)1.0 d
C)3.0 d
D)6.3 d
E)8.0 h

Question 17

If the mass of a planet is doubled while its radius and the radius of orbit of its moon remain constant,the speed of the moon is

A)increased by a factor of .
B)increased by a factor of 2.
C)not changed.
D)reduced by a factor of .
E)reduced by a factor of 2.

Question 18

Which of the following statements is one of Kepler's three laws of planetary motion?

A)A line joining any planet to the sun sweeps out equal areas in equal times.
B)Only an odd number of planets can orbit the sun.
C)The period of any planet about the sun is proportional to the planet's distance from the sun.
D)All planets move in elliptical orbits with Earth at one focus.
E)F = GMm/R²

Question 19

A woman whose weight on Earth is 500 N is lifted to a height of two Earth radii above the surface of Earth.Her weight

A)decreases to one-half of the original amount.
B)decreases to one-quarter of the original amount.
C)decreases to one-fifth of the original amount.
D)decreases to one-third of the original amount.
E)decreases to one-ninth of the original amount.

Question 20

You are in a spaceship that has a mass of 13 $\times$ 10⁴ kg and is 2.2 $\times$ 10¹² m from a black hole near the center of the galaxy.The gravitational force exerted by the black hole on the spaceship is 46 N.The force on the ship when it has moved to one-third of its original distance from the black hole is

A)410 N
B)140 N
C)150 N
D)5.0 N
E)730 N

Question 21

The constant of universal gravitation is

A)~9.81 m/s²
B)~6.67 $\times$ 10^-11 N · m²/kg²
C)~the gravitational attraction between the masses of any two bodies.
D)~the ratio of the forces of attraction between any two masses.
E)None of these is correct.

Question 22

You need an expression for the acceleration of the moon toward Earth.If the mass of the earth is M_e,the mass of the moon M_m,the separation of Earth and moon r,and the appropriate gravitational constant is G,the correct expression for the moon's acceleration is

A)GM_eM_m/r²
B)GM_eM_m²/r²
C)GM_m/r²
D)GM_e/r²
E)GM_e/r²M_m

Question 23

If a planet has a mass twice that of Earth and a radius four times that of Earth,the ratio of the acceleration due to gravity on the planet to that on Earth is

A)1/8
B)1/2
C)1/16
D)2/1
E)12/1

Question 24

Suppose a planet exists that has half the mass of Earth and half its radius.On the surface of that planet,the acceleration due to gravity is

A)twice that on Earth.
B)the same as that on Earth.
C)half that on Earth.
D)one-fourth that on Earth.
E)none of these.

Question 25

In the SI system,the units for gravitational field are

A)kg · m/s²
B)m/s²
C)kg²/m²
D)N/m
E)None of these is correct.

Question 26

Newton's law of gravity is F = GMm/r².What are the SI units of the gravitational constant G?

A)G has no dimensions
B)N · kg²/m²
C)N · m²/kg²
D)kg²/N · m²
E)None of these is correct.

Question 27

When a falling meteor is at a distance of twice Earth's radius (r_e = 6.436 $\times$ 10⁶ m)from the surface of Earth,its acceleration due to gravity is approximately

A)9.80 m/s²
B)4.90 m/s²
C)3.27 m/s²
D)2.45 m/s²
E)1.09 m/s²

Question 28

According to Newton's law of universal gravitation,if the distance between two bodies is tripled,the gravitational force between them is

A)unchanged.
B)halved.
C)doubled.
D)reduced to 1/3 its previous value.
E)None of these is correct.

Question 29

A planet is made of two distinct materials in two layers.From the core to R/2,the density of the material is 4000 kg/m³,and from R/2 to R the density is 3000 kg/m³.What is the mass of the planet if R = 5000 km?

A)2.62 $\times$ 10²³ kg
B)1.37 $\times$ 10²⁴ kg
C)1.64 $\times$ 10²⁴ kg
D)1.57 $\times$ 10²⁴ kg
E)1.87 $\times$ 10²⁴ kg

Question 30

At the surface of the moon,the acceleration due to the gravity of the moon is .At a distance from the center of the moon equal to three times the radius of the moon,the acceleration due to the gravity of the moon is

A)9
B) /3
C) /4
D) /9
E)27

Question 31

Kepler's second law,"a line joining any planet to the Sun sweeps out equal areas in equal times" is based on which conservation principle?

A)conservation of energy
B)conservation of linear momentum
C)conservation of angular momentum
D)the work-energy theorem
E)It is not based on any conservation principle.

Question 32

A planet is made of two distinct materials.From the core to R/2,the density of the material is 4000 kg/m³,and from R/2 to R the density is 3000 kg/m³.What is the gravity at the surface of the planet if R = 5000 km?

A)0.699 m/s²
B)3.66 m/s²
C)4.19 m/s²
D)4.38 m/s²
E)4.99 m/s²

Question 33

The Cavendish experiment has been described in elementary textbooks as "weighing the Earth." In fact,it was designed to measure the

A)acceleration due to gravity.
B)mass of Earth.
C)period of an Earth satellite.
D)gravitational constant G.
E)variation of g with height.

Question 34

A certain object weighs 22.2 N on the surface of Earth.If the radius of the moon is 0.276 times the radius of Earth and the mass of the moon is 0.0123 times the mass of Earth,the object's weight on the surface of the moon is approximately

A)0.365 N
B)3.58 N
C)9.79 N
D)22.2 N
E)133 N

Question 35

When two masses are a distance R apart,each exerts a force of magnitude F on the other.When the distance between them is changed to 4R,the force is changed to

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

Question 36

Suppose the gravitational mass,m_G,and inertial mass,m_I,were not equivalent and 1m_G = 2 m_I.Near Earth's surface,the acceleration due to gravity would have a value of

A)4.905 m/s²
B)9.81 m/s²
C)14.7 m/s²
D)19.62 m/s²
E)24.53 m/s²

Question 37

The mean radius of Earth is about 6.436 $\times$ 10⁶ m.A satellite in a circular orbit 3.20 $\times$ 10⁶ m above the surface of Earth has an acceleration of approximately

A)39.2 m/s²
B)22.1 m/s²
C)14.2 m/s²
D)6.54 m/s²
E)4.36 m/s²

Question 38

If the mass of Earth is 6 $\times$ 10²⁴ kg,the mass of the moon 7 $\times$ 10²² kg,the radius of the moon's orbit 4 $\times$ 10⁸ m,and the value of the gravitational constant 6 $\times$ 10^-11 N · m²/kg²,the force between Earth and the moon is approximately

A)5 $\times$ 10⁴ N
B)2 $\times$ 10²⁰ N
C)3 $\times$ 10⁵⁰ N
D)7 $\times$ 10³⁰ N
E)3 $\times$ 10²⁸ N

Question 39

The acceleration due to gravity in the vicinity of Earth

A)varies directly with the distance from the center of Earth.
B)is a constant that is independent of altitude.
C)varies inversely with the distance from the center of Earth.
D)varies inversely with the square of the distance from the center of Earth.
E)is described by none of these.

Question 40

An object weighs 37.0 N on Earth.If the mass of the moon is one eighty-first that of Earth and its radius one-fourth that of Earth,the weight of this object on the moon would be

A)1.77 N
B)7.10 N
C)18.2 N
D)28.3 N
E)37.0 N

Question 41

If the mass of a planet is doubled with no increase in its size,the escape speed for that planet is

A)increased by a factor of 1.4.
B)increased by a factor of 2.
C)not changed.
D)reduced by a factor of 1.4.
E)reduced by a factor of 2.

Question 42

A satellite with a mass m is in a stable circular orbit about a planet with a mass M.The universal gravitational constant is G.The radius of the orbit is R.The ratio of the potential energy of the satellite to its kinetic energy is

A)-2R
B)+2G
C)-2G/R
D)-2
E)2G/R

Question 43

NASA trains astronauts in "zero-g" by flying a C-9 jet plane in a parabolic path,the so called "Weightless Wonder" or the "Vomit Comet" flights.One path the plane takes is expressed as y = y_o + 0.8 x - 2.18 $\times$ 10^-4 x² where y_o is the highest point,and x and y are the horizontal and vertical coordinates (in m).What is the horizontal speed of the plane?

A)50 m/s
B)100 m/s
C)150 m/s
D)200 m/s
E)250 m/s

Question 44

Use the following scenario to answer the next problem.
NASA's "Weightless Wonder" flights can simulate "zero-g" or some other extraterrestrial gravity by flying a C-9 jet plane in a parabolic path.One path the plane takes is expressed as y = y_o + 0.8x – 1.02 x10^-4 x² where y_o is the highest point, and x and y are the horizontal and vertical coordinates (in m).
What is the horizontal speed of the plane if the flight is to simulate lunar gravity, g_Moon = 1.62 m/s².

A)50 m/s
B)100 m/s
C)150 m/s
D)200 m/s
E)250 m/s

Question 45

Suppose a rocket is fired vertically upward from the surface of Earth with one-half of the escape speed.How far from the center of Earth will it reach before it begins to fall back? (Let g = 9.8 m/s² and R_E = 6370 km.)

A)1.3 $\times$ 10⁴ km
B)8.5 $\times$ 10³ km
C)9.6 $\times$ 10³ km
D)2.6 $\times$ 10⁴ km
E)1.9 $\times$ 10⁴ km

Question 46

Use the following scenario to answer the next problem.
NASA's "Weightless Wonder" flights can simulate "zero-g" or some other extraterrestrial gravity by flying a C-9 jet plane in a parabolic path.One path the plane takes is expressed as y = y_o + 0.8x – 1.02 x10^-4 x² where y_o is the highest point, and x and y are the horizontal and vertical coordinates (in m).
Suppose y_o = 10000 m and the lowest height is 2000 m,how long is the flight with a simulated lunar gravity g_Moon = 1.62 m/s²?

A)44 s
B)100 s
C)40 s
D)60 s
E)66 s

Question 47

With what velocity must a body be projected vertically upward from the earth's surface,in the absence of friction,to rise to a height equal to the earth's radius (6400 km)?

A)4.3 $\times$ 10⁵ m/s
B)2.6 $\times$ 10³ m/s
C)10⁵ m/s
D)3.6 $\times$ 10² m/s
E)7.9 $\times$ 10³ m/s

Question 48

Taking the zero of potential energy to be at the infinite separation of two masses,consider the energy of a body in circular planetary motion.Which of the following statements is valid?

A)The total mechanical energy of the system is constant and negative.
B)The total mechanical energy of the system is constant and positive.
C)The potential energy of the system is equal to the kinetic energy but opposite in sign.
D)The potential energy of the system decreases as the radius of the orbit increases.
E)None of these is valid.

Question 49

Of the five masses in orbit around the central mass,the one that would require the most energy to escape from its orbit is

A)1
B)2
C)3
D)4
E)5

Question 50

A satellite whose mass is 1000 kg is in a circular orbit 1000 km above the surface of the earth.A space scientist wants to transfer the satellite to a circular orbit 1500 km above the surface.The amount of work that must be done to accomplish this is

A)3.43 GJ
B)1.71 GJ
C)-1.71 GJ
D)66.5 GJ
E)-3.43 GJ

Question 51

The radius of the moon is R.A satellite orbiting the moon in a circular orbit has an acceleration due to the moon's gravity of 0.14 m/s².The acceleration due to gravity at the moon's surface is 1.62 m/s².The height of the satellite above the moon's surface is

A)3.4R
B)0.42R
C)11R
D)2.4R
E)1.7R

Question 52

In the absence of air resistance,the least speed with which a body must be projected vertically upward from Earth's surface (m_e = 5.99 $\times$ 10²⁴ kg, r_e = 6.37 $\times$ 10⁶ m)if it is to reach an altitude of 800 km is

A)~1.39 $\times$ 10⁷ m/s
B)~3.73 $\times$ 10³ m/s
C)~1.57 $\times$ 10⁷ m/s
D)~3.96 $\times$ 10³ m/s
E)None of these is correct.

Question 53

A spring scale and a balance are used to "weigh" a body at the equator and later at a higher latitude,which has a different value for the acceleration due to gravity.Which of the following is a true statement concerning these weightings?

A)The readings of the spring scale are the same.The readings of the balance are the same.
B)The readings of the spring scale are different.The readings of the balance are different.
C)The readings of the spring scale are the same.The readings of the balance are different.
D)The readings of the spring scale are different.The readings of the balance are the same.
E)None of these is true.

Question 54

What is the escape speed from the sun,beginning (from rest relative to the sun)at the orbit of Earth,R = 1.50 $\times$ 10⁸ km.(Given: G = 6.67 $\times$ 10^-11 N · m²/kg²; mass of the sun = 2.0 $\times$ 10³⁰ kg.)

A)3.0 $\times$ 10⁴ m/s
B)2.1 $\times$ 10⁴ m/s
C)1.3 $\times$ 10⁶ m/s
D)9.4 $\times$ 10⁵ m/s
E)4.2 $\times$ 10⁴ m/s

Question 55

Four identical masses,each of mass M,are placed at the corners of a square of side L.The total potential energy of the masses is equal to -xGM ²/L,where x equals

A)4
B)
C)
D)
E)

Question 56

A plot of the gravitational potential energy of a 1-kg body as a function of its height above the surface of a planet shows that the gravitational acceleration at the surface of the planet is

A)1.5 m/s²
B)1.7 m/s²
C)3.0 m/s²
D)6.0 m/s²
E)9.8 m/s²

Question 57

The mass of Earth is M_E = 6.0 $\times$ 10²⁴ kg,and the mass of the Sun is 2.0 $\times$ 10³⁰ kg.They are a distance of 1.5 $\times$ 10⁸ km apart.Calculate the acceleration of Earth due to the gravitational attraction of the Sun.(G = 6.67 $\times$ 10^-11 N·m²/kg²)

A)1.8 $\times$ 10^-8 m/s²
B)6.0 $\times$ 10^-3 m/s²
C)9.8 m/s²
D)6.0 m/s²
E)6.0 $\times$ 10³ m/s²

Question 58

If we neglect the effects of air resistance,the impact speed of a body of mass m released from rest at an altitude of 2 $\times$ 10⁸ m above the surface of Earth (m_e = 5.99 $\times$ 10²⁴ kg,r_e = 6.37 $\times$ 10⁶ m)is

A)~3.92 $\times$ 10⁹ m/s
B)~6.26 $\times$ 10⁴ m/s
C)~1.10 $\times$ 10⁴ m/s
D)~1.21 $\times$ 10⁸ m/s
E)None of these is correct.

Question 59

Two satellites,one in geosynchronous orbit (T = 24 hrs)and one with a period of 12 hrs,are orbiting Earth.How many times larger than the radius of Earth is the distance between the orbits of the two satellites.(Mass(Earth)= 5.98 $\times$ 10²⁴ kg,G = 6.67 $\times$ 10^-11 N·m²,g = 9.81 m/s²,radius(Earth)= 6.38 $\times$ 10⁶ m)

A)0.51
B)2.0
C)6.6
D)5.7
E)none of the above

Question 60

One day a human being will land on Mars.Mars has a diameter of 6786 km and a mass of 6.42 $\times$ 10²³ kg.If you weighed 834 N on Earth,how much would you weigh on Mars?

A)1270 N
B)316 N
C)224 N
D)834 N
E)None of the above

Question 61

Suppose that a satellite is in a circular orbit at a height of 2.00 $\times$ 10⁶ m above Earth's surface.What is the speed of a satellite in this orbit?

A)8.31 $\times$ 10¹ m/s
B)6.90 $\times$ 10³ m/s
C)4.76 $\times$ 10⁷ m/s
D)9.62 $\times$ 10⁴ m/s
E)None of these is correct.

Question 62

Two objects with masses M₁ = 30,000 kg and M₂ = 70,000 kg are initially very far apart and at rest.If due to gravitational attraction the two objects attract each other,calculate their total kinetic energy when they are 100 km apart.

A)1.4 $\times$ 10^-3 J
B)1.4 $\times$ 10^-11 J
C)1.4 $\times$ 10^-6 J
D)0.7 $\times$ 10^-3 J
E)0.7 $\times$ 10^-6 J

Question 63

A body experiences a gravitational force with a magnitude of 200 N in a region of space where the magnitude of the gravitational field is 10 m/s².The mass of the body is

A)0.2 kg
B)100 kg
C)5 kg
D)20 kg
E)2000 kg

Question 64

A body experiences a gravitational force with a magnitude of 100 N in a region of space where the magnitude of the gravitational field is 20 m/s².The mass of the body is

A)0.2 kg
B)20 kg
C)5 kg
D)100 kg
E)2000 kg

Question 65

A satellite of 1000 kg is in a circular orbit at a height of R_E above the surface of Earth.Calculate the minimum energy required to put such a satellite into this orbit.(R_E = 6.38 $\times$ 10⁶ m,M_E = 5.98 $\times$ 10²⁴ kg,G = 6.67 $\times$ 10^-11 N·m²/kg²)

A)3.13 $\times$ 10¹⁰ J
B)8.34 $\times$ 10¹⁰ J
C)4.69 $\times$ 10¹⁰ J
D)6.25 $\times$ 10¹⁰ J
E)1.56 $\times$ 10¹⁰ J

Question 66

The mass and radius of the planet Venus are 81% and 95% that of Earth,respectively.How much faster or slower (as a percentage)is the escape velocity from Venus compared to that of Earth?

A)8% slower
B)8% faster
C)12% slower
D)12% faster
E)17% slower

Question 67

During the lunar mission of Apollo 11,Armstrong and Aldrin descended to the moon's surface in the lunar module while Collins remained in orbit in the command module.If the command module's period was 2 hours and 20 minutes,how high above the moon's surface did it orbit? (m_moon = 7.35 $\times$ 10²² kg,R_moon = 1.74 $\times$ 10⁶ m,and G = 6.67 $\times$ 10^-11 N · m²/kg².)

A)3.22 $\times$ 10⁵ m
B)1.04 $\times$ 10¹¹ m
C)5.67 $\times$ 10² m
D)2.53 $\times$ 10³ m
E)Not enough information is given to answer this question.

Question 68

As a satellite falls into a lower orbit,its speed _______.

A)decreases
B)is unchanged
C)increases
D)depends on the mass of the satellites
E)cannot tell

Question 69

An object whose mass is 4 kg experiences a gravitational force of 20 N at some point P.The gravitational field at this point is

A)5 m/s²
B)4 m/s²
C)-5 m/s²
D)20 n/kg
E)80 N/kg

Question 70

A satellite is orbiting Earth in an elliptical orbit.The distance of the satellite from Earth at the aphelion (r_A)is twice that at the perihelion (r_B).The total energy (potential and kinetic)of the satellite at A is _____ the total energy at B.

A)the same as
B)twice
C)half
D)one quarter
E)four times

Question 71

Two satellites of the same mass are placed in orbits around Earth.Satellite One is at an altitude of 1R_E and Satellite Two at an altitude of 2R_E where R_E = 6370 km is the radius of Earth.What is the ratio of the potential energy of Satellite One to Satellite Two?

A)
B)2/3
C)3/2
D)
E)2

Question 72

A satellite in circular orbit 1.609 $\times$ 10⁶ m above the surface of Earth (r_e = 6.436 $\times$ 10⁶ m)has an acceleration toward Earth of

A)9.76 m/s²
B)6.25 m/s²
C)7.80 m/s²
D)8.73 m/s²
E)15.3 m/s²

Question 73

A rocket is launched straight up from the surface of Earth with a speed v,such that the rocket reaches a maximum height of R_{E above} the surface.Find the launch speed of the rocket.Neglect air resistance.(R_E = 6.38 $\times$ 10⁶ m,M_E = 5.98 $\times$ 10²⁴ kg,G = 6.67 $\times$ 10^-11 N·m²/kg²)

A)2.81 km/s
B)5.59 km/s
C)11.2 km/s
D)7.91 km/s
E)None of the above

Question 74

Test masses are used to measure the gravitational field at various positions in and near a hollow spherical shell.The gravitational field will be smallest at point(s)

A)5
B)4
C)3
D)1,2,and 5
E)1 and 2

Question 75

A space rocket is launched such that very far from Earth it has a speed of 20 km/s.What was its initial launch speed from the surface of Earth? (R_E = 6.38 $\times$ 10⁶ m,M_E = 5.98 $\times$ 10²⁴ kg,G = 6.67 $\times$ 10^-11 N·m²/kg²)

A)22.9 km/s
B)20.0 km/s
C)45.8 km/s
D)21.5 km/s
E)25.5 km/s

Question 76

If the mass and radius of Mars to Earth are 11% and 53% respectively,calculate the ratio of the escape velocity of Earth divided by that of Mars.

A)4.8
B)2.2
C)0.5
D)6.6
E)1.6

Question 77

Suppose that a satellite is in a circular orbit at a height of 2.00 $\times$ 10⁶ m above Earth's surface.What is the period of the satellite's motion at this elevation?

A)5.65 h
B)4.24 h
C)1.07 h
D)2.12 h
E)None of these is correct.

Question 78

The radius R of a stable,circular orbit for a satellite of mass m and velocity v about a planet of mass M is given by

A)R = Gv/M
B)R = Gv/mM
C)R = GmM/v
D)R = GM/mv
E)R = GM/v²

Question 79

Suppose that a satellite is in a circular orbit at a height of 2.00 $\times$ 10⁶ m above Earth's surface.What is the acceleration due to gravity at this elevation?

A)9.80 m/s²
B)3.22 m/s²
C)5.67 m/s²
D)7.68 m/s²
E)None of these is correct.

Question 80

An object whose mass is 6 kg experiences a gravitational force of 30 N at some point P.The gravitational field at this point is

A)6 m/s²
B)5 m/s²
C)180 m/s²
D)30 N/kg
E)36 N/kg