# Quiz 11: Gravity

Physics & Astronomy

Q 1Q 1

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 10

^{11}m? A) 6.4 10^{11}m B) 1.8 10^{12}m C) 2.7 10^{12}m D) 1.1 10^{13}m E) 9.9 10^{13}mFree

Multiple Choice

C

Q 2Q 2

The moon has a period of 27.3 d and is an average distance from Earth of
3)84 10

^{5}km. A communications satellite is placed in an Earth orbit at 4.23 10^{4}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 hFree

Multiple Choice

B

Q 3Q 3

In a distant galaxy, a planet orbits its sun at a distance of 1.8 10

^{12}m with a period of 10^{8}s. A second planet orbits the same sun at a distance of 9 10^{11}m. What is the period of the second planet? A) 5 10^{7}s B) 2 10^{8}s C) 0.35 10^{8}s D) 2.8 10^{8}s E) 5 10^{8}sFree

Multiple Choice

C

Q 4Q 4

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.

Free

Multiple Choice

Q 5Q 5

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/R

^{2 }Free

Multiple Choice

Q 6Q 6

Of the satellites shown revolving around Earth, the one with the greatest speed is
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 7Q 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

Free

Multiple Choice

Q 8Q 8

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.

Free

Multiple Choice

Q 9Q 9

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 10

^{6}km) A) 1.5 yr B) 0.53 yr C) 0.28 yr D) 1.9 yr E) 3.5 yrFree

Multiple Choice

Q 10Q 10

The radius of the orbit of Earth around the Sun is 150 10

^{6}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 AUFree

Multiple Choice

Q 11Q 11

Use the figure to the right to answer the next problems. 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}Free

Multiple Choice

Q 12Q 12

Use the figure to the right to answer the next problems. 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

Free

Multiple Choice

Q 13Q 13

Use the figure to the right to answer the next problems. The orbits of two planets orbiting a star are shown. The semimajor axis of planet A is twice that of planet B.
-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.

Free

Multiple Choice

Q 14Q 14

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

Free

Multiple Choice

Q 15Q 15

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.

Free

Multiple Choice

Q 16Q 16

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/s

^{2}at sea level. The radius of Earth at sea level is 6.37 10^{6}m. The deepest trench is the Marianas Trench, south of Guam, which has a depth D = 1.103 10^{4}m below sea level. The highest mountain is Everest in Nepal, which has a height of h = 8.847 10^{3}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 NFree

Multiple Choice

Q 17Q 17

What is the force of gravity between the proton and electron in a hydrogen atom, given that G = 6.67 10

^{-11}N·m^{2}/kg^{2}, mass of a proton = 1.67 10^{-27}kg, mass of an Electron = 9.1 10^{-31}kg, and average radius of the electron's orbit in the hydrogen atom = 0.0529 nm? A) 1.9 10^{-57}N B) 1.9 10^{-54}N C) 3.6 10^{-53}N D) 3.6 10^{-47}N E) 3.6 10^{-41}NFree

Multiple Choice

Q 18Q 18

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.

Free

Multiple Choice

Q 19Q 19

You are in a spaceship that has a mass of 13 10

^{4}kg and is 2.2 10^{12}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 NFree

Multiple Choice

Q 20Q 20

Two planets have masses M and m, and the ratio M/m = 25. The distance between the planets is R. The point P, is between the planets as shown, and the distance between M and P is x. At P the gravitational forces on an object due to M and m are equal in magnitude. The value of x is
A) 5R/6
B) 25R/36
C) R/25
D) 6R/5
E) None of these is correct.

Free

Multiple Choice

Q 21Q 21

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.Free

Multiple Choice

Q 22Q 22

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

Free

Multiple Choice

Q 23Q 23

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.

Free

Multiple Choice

Q 24Q 24

In the SI system, the units for gravitational field are
A) kg · m/s

^{2 }B) m/s^{2 }C) kg^{2}/m^{2 }D) N/m E) None of these is correct.Free

Multiple Choice

Q 25Q 25

Newton's law of gravity is F = GMm/r

^{2}. What are the SI units of the gravitational constant G? A) G has no dimensions B) N · kg^{2}/m^{2 }C) N · m^{2}/kg^{2 }D) kg^{2}/N · m^{2 }E) None of these is correct.Free

Multiple Choice

Q 26Q 26

If the mass of Earth is 6 10

^{24}kg, the mass of the moon 7 10^{22}kg, the radius of the moon's orbit 4 10^{8}m, and the value of the gravitational constant 6 10^{-11}N · m^{2}/kg^{2}, the force between Earth and the moon is approximately A) 5 10^{4}N B) 2 10^{20}N C) 3 10^{50}N D) 7 10^{30}N E) 3 10^{28}NFree

Multiple Choice

Q 27Q 27

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/s^{2}B) 9.81 m/s^{2}C) 14.7 m/s^{2}D) 19.62 m/s^{2}E) 24.53 m/s^{2}Free

Multiple Choice

Q 28Q 28

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.

Free

Multiple Choice

Q 29Q 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/m

^{3}, and from R/2 to R the density is 3000 kg/m^{3}. What is the mass of the planet if R = 5000 km? A) 2.62 10^{2}^{3}kg B) 1.37 10^{24}kg C) 1.64 10^{24}kg D) 1.57 10^{24}kg E) 1.87 10^{24}kgFree

Multiple Choice

Q 30Q 30

A planet is made of two distinct materials. From the core to R/2, the density of the material is 4000 kg/m

^{3}, and from R/2 to R the density is 3000 kg/m^{3}. What is the gravity at the surface of the planet if R = 5000 km? A) 0.699 m/s^{2}B) 3.66 m/s^{2}C) 4.19 m/s^{2}D) 4.38 m/s^{2}E) 4.99 m/s^{2}Free

Multiple Choice

Q 31Q 31

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_{e}M_{m}/r^{2 }B) GM_{e}M_{m}^{2}/r^{2 }C) GM_{m}/r^{2 }D) GM_{e}/r^{2 }E) GM_{e}/r^{2}M_{m }Free

Multiple Choice

Q 32Q 32

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.

Free

Multiple Choice

Q 33Q 33

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

Free

Multiple Choice

Q 34Q 34

When a falling meteor is at a distance of twice Earth's radius (r

_{e}= 6.436 10^{6}m) from the surface of Earth, its acceleration due to gravity is approximately A) 9.80 m/s^{2 }B) 4.90 m/s^{2 }C) 3.27 m/s^{2 }D) 2.45 m/s^{2 }E) 1.09 m/s^{2 }Free

Multiple Choice

Q 35Q 35

The mean radius of Earth is about 6.436 10

^{6}m. A satellite in a circular orbit 3.20 10^{6}m above the surface of Earth has an acceleration of approximately A) 39.2 m/s^{2 }B) 22.1 m/s^{2 }C) 14.2 m/s^{2 }D) 6.54 m/s^{2 }E) 4.36 m/s^{2 }Free

Multiple Choice

Q 36Q 36

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

Free

Multiple Choice

Q 37Q 37

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.

Free

Multiple Choice

Q 38Q 38

The constant of universal gravitation is
A) ~9.81 m/s

^{2 }B) ~6.67 10^{-11}N · m^{2}/kg^{2 }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.Free

Multiple Choice

Q 39Q 39

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.

Free

Multiple Choice

Q 40Q 40

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

Free

Multiple Choice

Q 41Q 41

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

Free

Multiple Choice

Q 42Q 42

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.

Free

Multiple Choice

Q 43Q 43

Five homogeneous planets have relative masses and sizes as shown in the figure. A body of mass m would weigh least on which planet?
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 44Q 44

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 10

^{24}kg, G = 6.67 10^{-11}N·m^{2}, g = 9.81 m/s^{2}, radius(Earth) = 6.38 10^{6 }m) A) 0.51 B) 2.0 C) 6.6 D) 5.7 E) none of the aboveFree

Multiple Choice

Q 45Q 45

The mass of Earth is M

_{E}= 6.0 10^{24}kg, and the mass of the Sun is 2.0 10^{30}kg. They are a distance of 1.5 10^{8}km apart. Calculate the acceleration of Earth due to the gravitational attraction of the Sun. (G = 6.67 10^{-11}N·m^{2}/kg^{2}) A) 1.8 10^{-8}m/s^{2 }B) 6.0 10^{-3}m/s^{2 }C) 9.8 m/s^{2 }D) 6.0 m/s^{2 }E) 6.0 10^{3}m/s^{2 }Free

Multiple Choice

Q 46Q 46

One day a human being will land on Mars. Mars has a diameter of 6786 km and a mass of 6.42 10

^{23 }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 aboveFree

Multiple Choice

Q 47Q 47

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 10^{-4}x^{2}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/sFree

Multiple Choice

Q 48Q 48

Use the following scenario to answer the next problems.
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}+ 0.8 x - 1.02 10^{-4}x^{2}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/s^{2}. A) 50 m/s B) 100 m/s C) 150 m/s D) 200 m/s E) 250 m/sFree

Multiple Choice

Q 49Q 49

Use the following scenario to answer the next problems.
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}+ 0.8 x - 1.02 10^{-4}x^{2}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/s^{2}? A) 44 s B) 100 s C) 40 s D) 60 s E) 66 sFree

Multiple Choice

Q 50Q 50

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.

Free

Multiple Choice

Q 51Q 51

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/s

^{2}and R_{E}= 6370 km.) A) 1.3 10^{4}km B) 8.5 10^{3}km C) 9.6 10^{3}km D) 2.6 10^{4}km E) 1.9 10^{4}kmFree

Multiple Choice

Q 52Q 52

What is the escape speed from the sun, beginning (from rest relative to the sun) at the orbit of Earth, R = 1.50 10

^{8}km. (Given: G = 6.67 10^{-11}N · m^{2}/kg^{2}; mass of the sun = 2.0 10^{30}kg.) A) 3.0 10^{4}m/s B) 2.1 10^{4}m/s C) 1.3 10^{6}m/s D) 9.4 10^{5}m/s E) 4.2 10^{4}m/sFree

Multiple Choice

Q 53Q 53

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

Free

Multiple Choice

Q 54Q 54

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/s

^{2 }B) 1.7 m/s^{2 }C) 3.0 m/s^{2 }D) 6.0 m/s^{2 }E) 9.8 m/s^{2 }Free

Multiple Choice

Q 55Q 55

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.

Free

Multiple Choice

Q 56Q 56

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 10

^{5}m/s B) 2.6 10^{3}m/s C) 10^{5}m/s D) 3.6 10^{2}m/s E) 7.9 10^{3}m/sFree

Multiple Choice

Q 57Q 57

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

Free

Multiple Choice

Q 58Q 58

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/s

^{2}. The acceleration due to gravity at the moon's surface is 1.62 m/s^{2}. The height of the satellite above the moon's surface is A) 3.4R B) 0.42R C) 11R D) 2.4R E) 1.7RFree

Multiple Choice

Q 59Q 59

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)Free

Multiple Choice

Q 60Q 60

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

Free

Multiple Choice

Q 61Q 61

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 10^{24}kg, R_{e}= 6.37 10^{6}m) if it is to reach an altitude of 800 km is A) ~1.39 10^{7}m/s B) ~3.73 10^{3}m/s C) ~1.57 10^{7}m/s D) ~3.96 10^{3}m/s E) None of these is correct.Free

Multiple Choice

Q 62Q 62

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 10

^{8}m above the surface of Earth (m_{e}= 5.99 10^{24}kg, r_{e}= 6.37 10^{6}m) is A) ~3.92 10^{9}m/s B) ~6.26 10^{4}m/s C) ~1.10 10^{4}m/s D) ~1.21 10^{8}m/s E) None of these is correct.Free

Multiple Choice

Q 63Q 63

Suppose that a satellite is in a circular orbit at a height of 2.00 10

^{6}m above Earth's surface. What is the speed of a satellite in this orbit? A) 8.31 10^{1}m/s B) 6.90 10^{3}m/s C) 4.76 10^{7}m/s D) 9.62 10^{4}m/s E) None of these is correct.Free

Multiple Choice

Q 64Q 64

Suppose that a satellite is in a circular orbit at a height of 2.00 10

^{6}m above Earth's surface. What is the acceleration due to gravity at this elevation? A) 9.80 m/s^{2 }B) 3.22 m/s^{2}^{ }C) 5.67 m/s^{2 }D) 7.68 m/s^{2 }E) None of these is correct.Free

Multiple Choice

Q 65Q 65

Suppose that a satellite is in a circular orbit at a height of 2.00 10

^{6}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.Free

Multiple Choice

Q 66Q 66

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 10^{22}kg, R_{moon}= 1.74 10^{6}m, and G = 6.67 10^{-11}N · m^{2}/kg^{2}.) A) 3.22 10^{5}m B) 1.04 10^{11}m C) 5.67 10^{2}m D) 2.53 10^{3}m E) Not enough information is given to answer this question.Free

Multiple Choice

Q 67Q 67

A satellite in circular orbit 1.609 10

^{6}m above the surface of Earth (r_{e}= 6.436 10^{6}m) has an acceleration toward Earth of A) 9.76 m/s^{2 }B) 6.25 m/s^{2 }C) 7.80 m/s^{2 }D) 8.73 m/s^{2 }E) 15.3 m/s^{2 }Free

Multiple Choice

Q 68Q 68

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/v

^{2 }Free

Multiple Choice

Q 69Q 69

Two objects with masses M

_{1}= 30,000 kg and M_{2}= 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 10^{-3}J B) 1.4 10^{-11}J C) 1.4 10^{-6}J D) 0.7 10^{-3}J E) 0.7 10^{-6}JFree

Multiple Choice

Q 70Q 70

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

Free

Multiple Choice

Q 71Q 71

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

Free

Multiple Choice

Q 72Q 72

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 10^{6}m, M_{E}= 5.98 10^{24}kg, G = 6.67 10^{-11}N·m^{2}/kg^{2}) A) 3.13 10^{10}J B) 8.34 10^{10}J C) 4.69 10^{10}J D) 6.25 10^{10}J E) 1.56 10^{10}JFree

Multiple Choice

Q 73Q 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 10^{6}m, M_{E}= 5.98 10^{24}kg, G = 6.67 10^{-11}N·m^{2}/kg^{2}) A) 2.81 km/s B) 5.59 km/s C) 11.2 km/s D) 7.91 km/s E) None of the aboveFree

Multiple Choice

Q 74Q 74

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 10^{6}m, M_{E}= 5.98 10^{24}kg, G = 6.67 10^{-11}N·m^{2}/kg^{2}) A) 22.9 km/s B) 20.0 km/s C) 45.8 km/s D) 21.5 km/s E) 25.5 km/sFree

Multiple Choice

Q 75Q 75

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

Free

Multiple Choice

Q 76Q 76

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) 2Free

Multiple Choice

Q 77Q 77

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 timesFree

Multiple Choice

Q 78Q 78

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/s

^{2}B) 4 m/s^{2}C) -5 m/s^{2}D) 20 n/kg E) 80 N/kgFree

Multiple Choice

Q 79Q 79

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/s

^{2}B) 5 m/s^{2}C) 180 m/s^{2}D) 30 N/kg E) 36 N/kgFree

Multiple Choice

Q 80Q 80

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/s

^{2}. The mass of the body is A) 0.2 kg B) 20 kg C) 5 kg D) 100 kg E) 2000 kgFree

Multiple Choice

Q 81Q 81

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/s

^{2}. The mass of the body is A) 0.2 kg B) 100 kg C) 5 kg D) 20 kg E) 2000 kgFree

Multiple Choice

Q 82Q 82

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

Free

Multiple Choice

Q 83Q 83

Test masses are used to measure the gravitational field at various positions in and near a hollow spherical shell. The gravitational field will have its greatest value at point(s)
A) 3
B) 4
C) 5
D) 1, 2, and 5
E) 1 and 2

Free

Multiple Choice

Q 84Q 84

Test masses are used to measure the gravitational field at various positions in and near a solid sphere of uniform density. The gravitational field will have its greatest value at point
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 85Q 85

Test masses are used to measure the gravitational field at various positions in and near a solid sphere of uniform density. The gravitational field will have its least value at point
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 86Q 86

The magnitude of the gravitational field at point P, due to the body of mass m, is (G = 6.67 10

^{-11}N·m^{2}/kg^{2}) A) 2.67 10^{-11}N/kg B) 2.67 10^{-12}N/kg C) 9.81 N/kg D) 5.34 10^{-11}N/kg E) None of these is correct.Free

Multiple Choice

Q 87Q 87

The magnitude of the gravitational field at point P, due to the body of mass m, is (G = 6.67 10

^{-11}N·m^{2}/kg^{2}) A) 6.67 10^{-13}N/kg B) 2.67 10^{-12}N/kg C) 3.34 10^{-11}m/s^{2 }D) 5.34 10^{-11}N/kg E) 3.34 10^{-12}m/s^{2 }Free

Multiple Choice

Q 88Q 88

Earth's gravitational field is given by . The total flux (field times area) for a spherical surface area A that encloses all the field lines is
A) 4GM

_{E}B) GM_{E}C) GM_{E}/4 D) 2GM_{E}E) 4GM_{E}Free

Multiple Choice

Q 89Q 89

The mass density of a planet varies with distance from the center as where C is a dimensionless constant, and R

_{P}is the radius of the planet. The gravitational field of the planet for r < R_{P}is A) B) C) D) E)Free

Multiple Choice

Q 90Q 90

The Roche Limit tells us about the point on a rotating planet where the gravitational force at the equator is just equal to the necessary centripetal force needed for rotation. Assuming the planet to be a uniform sphere of density 5520 kg/m

^{3}, find the shortest period of rotation possible before exceeding the Roche Limit. (G = 6.67 10^{-11}N·m^{2}/kg^{2}) A) none of the following B) 50 mins C) 150 mins D) 48 mins E) 85 minsFree

Multiple Choice