Deck 12: Gravitation

Question 1

In order for a satellite to be in a stable circular orbit a vertical distance h above the surface of the Earth,how fast must it be moving? In the answers,r = the radius of the Earth and m = the mass of the Earth.

A)
B)
C)
D)

Answer 1

Question 2

Two identical point masses are held a distance of 5.0 cm apart.One of the masses is released and allowed to fall toward the other mass.If its initial acceleration just as it is released is 1.67 * 10^-8 m/s²,what is the mass of one of these two identical point masses? Assume that the only force acting on the masses is the gravitational force of the other mass.

A)10 kg
B)0.63 kg
C)1.2 kg
D)0.59 kg

Answer 2

0.63 kg

Question 3

Two identical 30.0-kg spheres of diameter 20 cm are 50.0 cm apart (center to center distance).If they are released from rest and allowed to fall toward one another,what is their speed when they just make contact? Assume that the only force acting on the masses are the gravitational force of the other mass.

A)7.24 * 10^-4 m/s
B)1.10 * 10^-4 m/s
C)8.17 * 10^-4 m/s
D)7.75 * 10^-5 m/s
E)5.31 * 10^-4 m/s

Answer 3

7.75 * 10^-5 m/s

Question 4

Two identical 10.0-kg point masses are held a distance of 20.0 cm apart.If one of the masses is released and allowed to fall toward the other mass,what is the acceleration of the mass just as it is released? Assume that the only force acting on the masses is the gravitational force of the other mass.

A)0.330 * 10^-8 m/s².
B)1.67 * 10^-8 m/s².
C)3.41 * 10^-8 m/s².
D)4.83 * 10^-8 m/s².

Question 5

You are standing on the surface of a small spherical moon whose radius is 6.30 * 10⁴ m and mass of 8.00 * 10¹⁸ kg.An astronaut throws a rock of mass 5.00 kg straight upward with a speed 20.0 m/s.(This Moon is too small to have an atmosphere.)What maximum height above the surface of the Moon will the rock reach?

A)0.237 km
B)0.563 km
C)1.00 km
D)1.49 km
E)1.52 km

Question 6

Two objects aren't in contact,but they affect each other via the gravitational force,and there aren't any other forces acting on either object.Which statement is always true?

A)The magnitude of the gravitational force is the same on both objects.
B)The direction of the gravitational force is the same on both objects.
C)The magnitude of the acceleration is the same for both objects.
D)The direction of the acceleration is the same for both objects.

Question 7

The free fall acceleration at the altitude h is 9.00 m/s².If R is the radius of the Earth,then the altitude h is

A)0.400 R.
B)0.279 R.
C)0.184 R.
D)0.107 R.
E)0.0450 R.

Question 8

A spaceship is fired from the Earth's surface with a speed of v.The radius of the Earth is R,the mass of the Earth is M,and the universal gravitational constant is

A)
B)
C)
D)
E)It is impossible to determine.

Question 9

At what elevation above the Earth's surface is the acceleration due to gravity 1% less than it is at the surface? The radius of the Earth is 6.37 * 10⁶ m.

A)31.9 km
B)32.1 km
C)40.6 km
D)63.7 km

Question 10

A projectile is shot from the surface of Earth by means of a very powerful cannon.If the projectile reaches a height of 100.0 km above Earth's surface,what was the speed of the projectile when it left the cannon?

A)1036 m/s
B)1123 m/s
C)1265 m/s
D)1392 m/s
E)1409 m/s

Question 11

Four identical subatomic particles,each of mass m,are initially at rest and located on the four corners of a square,one at each corner.The length of each side of the square is L.There aren't any other forces on the particles besides the gravitational force.What is the magnitude of their initial accelerations?

A)Gm/L²
B)2Gm/L²
C)3Gm/L²
D)None are correct.

Question 12

A satellite is in a stable orbit at an elevation above the surface of the Earth equal to the radius of the Earth.An asteroid collides with the satellite.Both objects stop moving and fall straight down.How fast are the satellite and asteroid moving when they hit the surface of the Earth? In the answers,r = the radius of the Earth and m = the mass of the Earth.Ignore air resistance.

A)
B)
C)
D)None are correct.

Question 13

What is the magnitude of free fall acceleration at an altitude h = R where R is the radius of the Earth?

A)9.81 m/s²
B)4.90 m/s²
C)3.27 m/s²
D)2.45 m/s²
E)1.09 m/s²

Question 14

The acceleration due to gravity on the Earth's surface is g.At an elevation of 1,000 km above the Earth's surface is the acceleration due to gravity in terms of g? The radius of the Earth is 6.37 * 10⁶ m.

A)0.864g
B)0.747g
C)0g
D)0.452g

Question 15

Determine the minimum amount of energy that a projectile of mass 100.0 kg must gain to reach a circular orbit 10.00 km above the Earth's surface if launched from the equator.

A)6.236 * 10⁹ J
B)1.077 * 10⁷ J
C)6.244 * 10⁹ J
D)3.132 * 10⁹ J
E)3.121 * 10⁹ J

Question 16

A geostationary satellite is in a circular orbit around the Earth.What is the linear speed of the satellite?

A)4.6 * 10³ m/s
B)3.1 * 10³ m/s
C)7.6 * 10³ m/s
D)8.6 * 10³ m/s
E)9.6 * 10³ m/s

Question 17

A geostationary satellite is in a circular orbit around the Earth.What is the radius of the orbit of the satellite?

A)4.2 * 10⁴ km
B)2.3 * 10⁴ km
C)3.1 * 10⁴ km
D)6.7 * 10⁴ km
E)8.4 * 10⁴ km

Question 18

An imaginary planet has a mass of 8.00 * 10²³ kg and a diameter of 5.0 * 10⁶ m.What is the escape speed from the surface of this planet?

A)3.5 km/s
B)4.8 km/s
C)5.7 km/s
D)6.5 km/s
E)7.2 km/s

Question 19

A spaceship is fired from the Earth's surface with a speed of v.The radius of the Earth is R,the mass of the Earth is M,and the universal gravitational constant is

A)
B)
C)
D)
E)None are correct.

Question 20

A plumb bob located at latitude 63.0 ^$\circ$ north hangs motionlessly with respect to the ground beneath it.Determine the angle that the string supporting the bob makes with respect to a straight line going through the bob and the center of the Earth.

A)0 ^$\circ$
B)0.10 ^$\circ$
C)0.20 ^$\circ$
D)0.30 ^$\circ$
E)Sufficient information is not given.

Question 21

The peak of Mount Everest is 8840 m above sea level.Assuming that the Earth is a perfect sphere with a radius from the center to sea level of 6380 km,the gravitational acceleration at the peak of Mount Everest is

A)9.84 m/s².
B)9.81 m/s².
C)9.78 m/s².
D)9.76 m/s².
E)9.74 m/s².

Question 22

How much energy does it take to move a 300-kg satellite from an orbit 300 km above the Earth's surface to an orbit 600 km above the Earth's surface?

A)7.72 * 10⁸ J
B)3.86 * 10⁸ J
C)8.82 * 10⁸ J
D)4.35 * 10⁸ J
E)6.56 * 10⁸ J

Question 23

A 1000-kg satellite in circular orbit around the Earth is moving at a speed of 7 * 10³ m/s.How much work must be done to "raise" the satellite to a higher circular orbit doubling its height above the surface of the Earth?

A)4.4 * 10⁹ J
B)2.3 * 10¹¹ J
C)4.4 * 10¹¹ J
D)2.4 * 10¹⁰ J
E)4.5 * 10¹⁰ J

Question 24

The figure shows a system of three masses.What is the direction of the gravitational force on the 10-kg mass? The center-to-center distances between masses are shown in the diagram.

A)170.1 ^$\circ$
B)9.9 ^$\circ$
C)5.5 ^$\circ$
D)174.5º
E)164.5º

Question 25

For two identical satellites in circular motions around the Earth which statement is true?

A)The one in the lower orbit has less total energy.
B)The one in the higher orbit has more kinetic energy.
C)The one in the lower orbit has more total energy.
D)Both have the same total energy.

Question 26

The escape velocity of a rocket launched from position A,the center of the three planet system depicted in the figure is 12.6 km/s.Each planet has the same mass and radius R = 10⁶ m,and the center-to-center distance between any two planets is 10 R.What is the mass of one of the three planets?

A)1.00 * 10²⁴ kg
B)1.15 * 10²⁴ kg
C)7.81 * 10²⁴ kg
D)2.29 * 10²⁴ kg
E)3.56 * 10²⁴ kg

Question 27

The figure shows a system of three masses.What is the magnitude of the gravitational force on the 10-kg mass? The center-to-center distances between masses are shown in the diagram.

A)4.96 * 10^-8 N
B)4.10 * 10^-8 N
C)5.34 * 10^-8 N
D)6.56 * 10^-8 N
E)9.05 * 10^-8 N

Question 28

Satellites in low Earth orbit lose energy from collision with the tenuous atmosphere,causing them to slowly spiral inward.What happens to their kinetic energy as they fall inward?

A)It decreases.
B)It increases.
C)It remains constant.
D)It may either increase or decrease,depending on the particular spiral.

Question 29

The figure shows a system of three masses.If the 30-kg mass is released,what is the magnitude of its initial acceleration? The center-to-center distances between masses are shown in the diagram.

A)4.96 * 10^-9 m/s²
B)9.04 * 10^-9 m/s²
C)6.38 * 10^-9 m/s²
D)3.58 * 10^-9 m/s²
E)3.97 * 10^-9 m/s²

Question 30

Before the discovery of Pluto's moon,Charon,Pluto's mass was estimated to be around 6 * 10²² kg.If Charon orbits Pluto with a period of 153 hours at a distance of 1.75 * 10⁷m estimate the mass of Pluto.

A)3.15 * 10²¹ kg
B)3.18 * 10²² kg
C)1.04 * 10²² kg
D)1.14 * 10²² kg
E)6.31 * 10²² kg

Question 31

The radius of a black hole is the distance from the black hole's center at which the escape speed is the speed of light (c = 3.0 * 10⁸ m/s).What is the radius of a 24 solar mass black hole?

A)6.3 * 10⁶ m
B)7.1 * 10⁴ m
C)5.4 * 10⁵ m
D)7.0 * 10⁸ m
E)2.2 * 10⁷ m

Question 32

What is the difference in the acceleration due to gravity between your head and your feet.Assume your height is 1.80 m. Mass of the Earth: 5.98 * 10²⁴ kg
Radius of the Earth: 6.38 * 10⁶ m

A)Zero,they are exactly the same.
B)1.57 * 10^-7 m/s²
C)2.77 * 10^-6 m/s²
D)5.53 * 10^-6 m/s²
E)2.77 * 10^-3 m/s²

Question 33

What is the orbital velocity of a 100-kg satellite orbiting at an altitude of 1000 km above the surface of the Earth?

A)12430 m/s
B)7360 m/s
C)2450 m/s
D)5420 m/s
E)8760 m/s

Question 34

Determine the minimum amount of energy that a projectile of mass 100.0 kg must gain to reach a circular orbit 10.00 km above the Earth's surface if launched from the north pole.

A)6.236 * 10⁹ J
B)1.077 * 10⁹ J
C)3.132 * 10⁹ J
D)3.121 * 10⁹ J
E)6.244 * 10⁹ J

Question 35

Three masses that are 10 kg each are located at the corners of an equilateral triangle,with side length of 0.55 m.What is the magnitude of the total force acting on one mass due to the other two masses?

A)3.82 * 10^-8 N
B)1.56 * 10^-8 N
C)2.10 * 10^-8 N
D)2.21 * 10^-8 N
E)4.41 * 10^-8 N

Question 36

The escape velocity of a rocket launched from position A,the center of the three planet system depicted in the figure is 12.6 km/s.Each planet has mass M = 10²⁴ kg,radius R ,and the center-to-center distance between any two planets is 10 R.What is the radius of one of the three planets?

A)2.29 * 10⁶ m
B)1.00 * 10⁶ m
C)4.29 * 10⁶ m
D)4.37 * 10⁵ m
E)9.42 * 10⁵ m

Question 37

Two satellites A and B orbit the Earth with the orbital radius of A,R_A equal to twice that of B,R_A = 2R_B.What is the ratio of their masses M_A/M_B?

A)2
B)½
C)4
D)¼
E)It is impossible to tell.

Question 38

What is the escape velocity of a rocket launched from position A,the center of the three planet system depicted in the figure.Each planet has mass M = 10²⁴ kg,radius R = 10⁶ m,and the center-to-center distance between any two planets is 10 R.

A)1.04 km/s
B)8.33 km/s
C)2.35 km/s
D)12.6 km/s
E)3.96 km/s

Question 39

If the Earth suddenly stopped in its orbit around the Sun,it would fall into the Sun.Find the speed of the Earth as it impacted the Sun. Radius of the Sun: 6.96 * 10⁸ m
Radius of the Earth: 6.38 *10⁶ m
Initial distance between the Earth and the Sun: 1.50 * 10¹¹ m
Mass of the Earth: 5.98 * 10²⁴ kg
Mass of the Sun: 1.99 *10³⁰ kg

A)4.23 * 10⁴ m/s
B)4.33 * 10⁵ m/s
C)6.13 * 10⁵ m/s
D)6.19 * 10⁵ m/s
E)8.75 * 10⁵ m/s

Question 40

You wish to place a geo-stationary satellite to study Jupiter's Great Red Spot,how high above the surface must it be placed? Possibly useful information:
Mass of Jupiter: 1.90 * 10²⁷ kg
Radius of Jupiter: 7.15 * 10⁷ m
Rotational Period: 9.925 h

A)6.82 * 10⁵ m
B)1.95 * 10⁸ m
C)8.85 * 10⁷ m
D)4.10 * 10²⁴ m
E)2.66 * 10¹⁹ m

Question 41

When the Moon is directly between the Earth and the Sun,what is the ratio of the force on the Moon due to the Earth to the force on the Moon due to the Sun? The masses of Sun,Earth,and Moon are 1.99 * 10³⁰ kg,5.97 * 10²⁴ kg,and 7.36 * 10²² kg,respectively.The Earth-Moon distance is 3.84 *10⁸ m,while the Earth-Sun distance is 1.51 * 10¹¹ m.

A)2.2
B)0.46
C)847
D)1.2 * 10^-3

Question 42

A mass of 10 kg is taken up to a distance nine times the Earth's radius above the surface of the Earth.What is its weight in N at that point?

A)10
B)980
C)98
D)9.8
E)0.98

Question 43

The radius of the orbit of a planet around a star is proportional to

A)the orbital period of the planet.
B)the square root of the orbital period of the planet.
C)the square of the orbital period of the planet.
D)the 3/2 power of the orbital period of the planet.
E)the 2/3 power of the orbital period of the planet.

Question 44

A planet with a mass of 2.7 *10²² kg is in a circular orbit around a star with a mass of 5.3 * 10³² kg.If the planet has an orbital radius of 4.8 * 10⁹ m,what is its orbital period?

A)0.29 hours
B)0.43 hours
C)3.1 hours
D)25 years
E)49 years

Question 45

Two stars,S1 and S2,attract each other gravitationally with a force of magnitude

A)1/4CF.
B)1/2 F.
C)F.
D)2 F.
E)4 F.

Question 46

The following statements refer to man-made,artificial satellites in orbit around the Earth.Which one is true?

A)It is possible to have a satellite traveling either at high speed or at low speed in a given circular orbit.
B)Only circular orbits,not elliptical ones,are possible for artificial satellites.
C)A satellite of a large diameter circular orbit will always have a longer period of revolution than will a satellite with smaller diameter orbit.
D)The velocity required to keep a satellite in a given orbit depends on the mass of the satellite.
E)The period of revolution of a satellite is independent of the radius of its orbit.

Question 47

An astronaut on the surface of a strange planet observes that the acceleration of gravity is 7 m/s².What could be an explanation of this phenomenon?

A)The mass of the planet is the same as that of Earth,but the radius is smaller.
B)The mass of the planet is less than that of Earth,and the radius is the same.
C)The mass of the planet is less than that of Earth,and the radius is bigger.
D)The mass of the planet is more than that of Earth,and the radius is the same.
E)Both B and C could explain it.

Question 48

What is the escape speed from a spherical asteroid of radius 15 km,whose mass density is approximately half that of the Earth,or 2.8 g/cm³?

A)11m/s
B)16 m/s
C)19 m/s
D)2300 m/s
E)More information is needed.

Question 49

Given the mean distance between the Moon and the Earth is 3.84 * 10⁸ m,determine the magnitude of the gravitational force exerted by the Moon of mass 7.32 * 10²² kg on a 70-kg man standing on the surface of the Earth.

A)2.33 * 10^-3 N
B)5.89 * 10^-2 N
C)9.81 * 10^-2 N
D)0.75 N
E)5.2 N

Question 50

If the Earth's orbit around the Sun were increased to a radius twice what it is now.Which of the following is true?

A)The force of gravity on the Earth due to the Sun would decrease by a factor of four.
B)The force of gravity on the Earth due to the Sun would decrease by a factor of two.
C)The force of gravity on the Sun due to the Earth would decrease by a factor of four.
D)The force of gravity on the Sun due to the Earth would decrease by a factor of two.
E)Both A and C are true.

Question 51

Two rockets are launched from the surface of a planet.The first rocket has ten times the mass of the second rocket.Which statement is true?

A)The first rocket has greater escape velocity than the second rocket.
B)The first rocket has smaller escape velocity than the second rocket.
C)Both rockets have the same escape velocity.
D)Both rockets have the same kinetic energy.

Question 52

Which is larger in magnitude,the force of gravity of the Earth on the Moon,or the force of gravity of the Moon on the Earth?

A)The Earth exerts a larger force on the Moon.
B)The Moon exerts a larger force on the Earth.
C)The two forces are equal in magnitude.

Question 53

An artificial satellite of 10⁴ kg is orbiting the Earth's moon in an orbit of 100 km above its surface.It takes 118 minutes to complete one revolution.Assuming the Moon to be a uniform sphere,the density of the Moon is

A)7850 kg/m³.
B)5734 kg/m³.
C)4205 kg/m³.
D)3330 kg/m³.
E)2154 kg/m³.

Question 54

A ball of mass 2 kg is launched into a circular orbit close to the Earth's surface.Given the mass of Earth is M = 5.98 * 10²⁴ kg and its radius is 6.37 * 10⁶ m.Ignoring air resistance,the energy required to launch the ball from rest into the orbit is

A)3.14 * 10⁷ J.
B)6.25 * 10⁷ J.
C)9.8 * 10⁷ J.
D)11.5 * 10⁸ J.
E)6.28 * 10⁹ J.

Question 55

A particle of mass m is located at a distance r from the center of a sphere of mass M and radius R.The force on the particle as a function of distance r,inside the sphere is given by

A)-GMmr/R.
B)-GMmr/R².
C)-GMmr/R³.
D)-GMm/R².
E)-GMm/r².

Question 56

How far from Earth on a line between the Earth (5.97 * 10²⁴ kg)and the Moon (7.36 * 10²² kg)is the gravitational force on a spacecraft due to Earth and Moon equal to zero? Report as a fraction of the Earth-Moon distance.

A)99% of Earth-Moon distance
B)90% of Earth-Moon distance
C)81% of Earth-Moon distance
D)11% of Earth-Moon distance
E)1.2% of Earth-Moon distance

Question 57

The orbital period of a planet around a star is proportional to

A)the radius of the orbit.
B)the square root of the radius of the orbit.
C)the square of the radius of the orbit.
D)the 3/2 power of the radius of the orbit.
E)the 2/3 power of the radius of the orbit.

Question 58

The mass of Jupiter is 1.9 * 10²⁷ kg and its radius 7.14 * 10⁷ m.The gravitational field strength at its surface is

A)32.5 N/kg.
B)24.9 N/kg.
C)18.5 N/kg.
D)12.6 N/kg.
E)10.8 N/kg.

Question 59

The period of a particular satellite is exactly 24 hours.How high above the surface of the Earth is it orbiting? The Earth's mass is 5.97 * 10²⁴ kg,and the Earth's radius is 6378 km.

A)42.2 * 10³ km
B)35.8 * 10³ km
C)61.8 * 10³ km
D)55.4 * 10³ km
E)The mass of the satellite is needed.

Question 60

A space station is placed between a planet and its single moon at a position where the net force on the space station is zero.If the planet has a mass 1000 times larger than its moon,how far from the planet is the space station?

A)50.0% of the way to the moon
B)68.4% of the way to the moon
C)94.4% of the way to the moon
D)96.9% of the way to the moon
E)99.9% of the way to the moon

Question 61

If you quadruple the radius of the orbit of a moon around the planet Jupiter,the new time of revolution,T',of this moon is

A)1/2 T.
B)T.
C)2 T.
D)4 T.
E)8 T.

Question 62

A satellite orbits around the Earth.Which statement below is true? K = kinetic energy of the satellite
U = gravitational potential energy of the satellite

A)K > 0,U > 0
B)K > 0,U < 0
C)K < 0,U > 0
D)K < 0,U < 0
E)K > 0,U = 0

Question 63

Our Sun has a mass of M = 2.0·10³⁰ kg and a radius of R = 7·10⁸ m.What is the gravitational acceleration at the surface of the Sun?

A)0.213 m/s²
B)9.81 m/s²
C)21.3 m/s²
D)272 m/s²
E)3.82·10⁵ m/s²

Question 64

An asteroid has been discovered revolving around the Sun on a circular orbit with radius 4.2 times the radius of the Earth's orbit around the Sun (which is about 149.6 million kilometers).Knowing that it takes the Earth 1 year to complete a revolution,how many years does it take for that asteroid?

A)0.041
B)0.32
C)1
D)5.3
E)8.6

Question 65

What is the orbital speed of a satellite in a geostationary orbit about the Earth? (The necessary altitude above ground for a geo-stationary satellite is 35,800 km;the Earth's radius is 6400 km.)

A)5.3 km/s
B)15.7 km/s
C)3.1 km/s
D)12.1 km/s
E)8.2 km/s

Question 66

The distance between Earth and the Sun is 149.6 million km,and the distance between Venus and the Sun is 108.2 million km.How long does it take Venus to orbit once around the Sun?

A)0.615 years
B)0.723 years
C)1 year
D)1.38 years
E)1.63 years

Question 67

If two planets,A and B,have the same value of g on their surfaces,which of the following scenarios cannot be true? (M_A and M_B are their masses and R_A and R_B are their radii.)

A)M_A = 4 M_B and R_A = 2 R_B
B)M_A = 9 M_B and R_A = 3 R_B
C)M_A = 0.25 M_B and R_A = 0.5 R_B
D)M_A = M_B and R_A = R_B
E)M_A = 4 M_B and R_A = 3 R_B

Question 68

A 51-kg satellite is put into orbit and has 152 MJ of kinetic energy.How high above the Earth's surface is the orbit?

A)60,400 km
B)37,000 km
C)74,000 km
D)53,100 km
E)86,200 km

Question 69

A spherical planet has twice the mass and twice the radius of the Earth.If a man weighs 810 N on Earth,what would his weight be on the surface of that planet?

A)405 N
B)810 N
C)1215 N
D)1620 N
E)2025 N

Question 70

If the Earth became 5% bigger in radius (R = 1.05R_E)and 10% bigger in mass (M = 1.1M_E),about what would the new value of the acceleration of gravity be near the surface of the Earth?

A)g
B)1.3 g
C)0.7 g
D)2.0 g
E)0.1 g

Question 71

Two planets,A and B,are in orbit around the same star.If A has a period of 12 days and an orbit radius of 1.63·10⁵ km,and B has a radius of 3.26·10⁵ km,what is the period of B in days?

A)12·(1/2)^3/2
B)12·(2)^3/2
C)12·(1/2)^2/3
D)12·(2)^2/3
E)(1/2)^5/2/12

Question 72

A 51-kg satellite is put into orbit 37,000 km above the Earth's surface.What is its kinetic energy?

A)456.9 kJ
B)663.6 kJ
C)866.7 kJ
D)103.3 MJ
E)235.1 MJ

Question 73

A satellite is put into orbit 37,000 km above the Earth's surface and has a kinetic energy of 105 MJ.What is the mass of the satellite?

A)23 kg
B)51 kg
C)18 kg
D)32 kg
E)120 kg