Deck 10: Gravitation

Question 1

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 * 10²³ kg
B) 1.37 * 10²⁴ kg
C) 1.64 * 10²⁴ kg
D) 1.57 * 10²⁴ kg
E) 1.87 * 10²⁴ kg

Answer 1

1.64 * 10²⁴ kg

Question 2

The acceleration due to gravity near 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.

Answer 2

varies inversely with the square of the distance from the center of Earth.

Question 3

You are in a spaceship that has a mass of 13 *10⁴ kg and is 2.2 * 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.

Answer 3

410 N.

Question 4

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) R_E /9.

Question 5

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 6

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.

Question 7

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) 2/16.
E) 2/1.

Question 8

In the SI system, the units for gravitational field are

A) kg · m/s².
B) m/s².
C) kg²/m².
D) N/m.
E) kg/s².

Question 9

You need an expression for the acceleration of the Moon toward Earth. If the mass of 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 10

Suppose the gravitational mass, m_G, and inertial mass, m_I, were not equivalent and 1 m_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 11

Which of the graphs shows the magnitude of the gravitational force between two objects as a function of distance between their centers.

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

Question 12

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

A) 5 * 10⁴ N.
B) 2 * 10²⁰ N.
C) 3 * 10⁵⁰ N.
D) 7 * 10³⁰ N.
E) 3 * 10²⁸ N.

Question 13

What is the force of gravity between the proton and electron in a hydrogen atom, given that G = 6.67 * 10^-11 N m²/kg², 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 N

Question 14

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 15

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 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/s² at sea level. The radius of Earth at sea level is 6.37 * 10⁶ m. The deepest trench is the Marianas Trench, south of Guam, which has a depth d = 1.103 *10⁴ m below sea level. The highest mountain is Everest in Nepal, which has a height of h = 8.847 * 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 17

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) Gravitational force on an object is independent on its mass.

Question 18

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

A) G is dimensionless.
B) N kg²/m²
C) N m²/kg²
D) kg²/N • m²
E) N

Question 19

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 20

When a falling meteor is at a distance of twice Earth's radius r_e = 6.436 *0 10⁶ 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 21

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 22

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

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

Question 23

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

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

Question 24

A certain object has mass of 2.26 kg 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) 2.26 kg.
B) 3.58 N.
C) 0.364 kg.
D) 22.2 N.
E) 9.81 N.

Question 25

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) 7.30 N.
C) 18.2 N.
D) 28.3 N.
E) 37.0 N.

Question 26

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/m³, find the shortest period of rotation possible before exceeding the Roche limit G = 6.67* 10^-11 N · m²/kg²).

A) None of the following.
B) 50 min
C) 150 min
D) 48 min
E) 85 min

Question 27

The International Space Station ISS) orbits Earth about 350 km above the surface of Earth R_E = 6370 km). Determine the ratio of the gravitational force experienced by a 55.0 kg astronaut when boarding the ISS to the gravitational force experienced by the astronaut when on Earth.

A) 0
B) 0.50
C) 0.90
D) 0.95
E) 1.11

Question 28

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

Question 29

A plot of the gravitational potential energy of a 1.0-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) 2.7 m/s².
D) 6.0 m/s².
E) 9.8 m/s².

Question 30

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 31

The mean radius of Earth is about 6.436 *10⁶ m. A satellite in a circular orbit 3.20 * 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) 4.38 m/s².

Question 32

Suppose that a satellite is in a circular orbit at a height of 2.00 *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 33

One day a human being will land on Mars. Mars has a diameter of 6786 km and a mass of 6.42 * 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) 2200 N

Question 34

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) tripled.
C) reduced to 1/3 its previous value.
D) reduced to 1/9 its previous value.
E) increased by factor of 9.

Question 35

A satellite in circular orbit 1.609 * 10⁶ m above the surface of Earth r_e = 6.436 * 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 36

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 , and .)

A) 1.3 *10⁴ km
B) 8.5*10³ km
C) 9.6 *10³ km
D) 2.6 * 10⁴ km
E) 1.9 *10⁴ km

Question 37

The constant of universal gravitation is

A) ~9.81 m/s².
B) ~6.67 *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) dependent on the nearest mass.

Question 38

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 39

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 40

A satellite whose mass is 1000 kg is in a circular orbit 1000 km above the surface of 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) 11.9 GJ.
E) -3.43 GJ.

Question 41

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 42

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

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

Question 43

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 *10²⁴ kg, r_e = 6.37 * 10⁶ m) if it is to reach an altitude of 800 km is

A) ~1.39 * 10⁷ m/s.
B) ~3.73 * 10³ m/s.
C) ~1.57 * 10⁷ m/s.
D) ~3.96 * 10³ m/s.
E) ~3.34 * 10³ m/s.

Question 44

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 be determined

Question 45

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 * 10¹¹ m?

A) 6.4 * 10¹¹ m
B) 1.8 *10¹² m
C) 5.34 * 10⁶ m
D) 1.1 * 10¹³ m
E) 9.9 * 10¹³ m

Question 46

If we neglect the effects of air resistance, the impact speed of a body of mass m released from rest at an altitude of 2.00 *10⁸ m above the surface of Earth m_e = 5.99 *10²⁴ kg, r_e = 6.37 *10⁶ m) is

A) ~3.92 * 10⁹ m/s.
B) ~6.26 *10⁴ m/s.
C) ~1.10 * 10⁴ m/s.
D) ~1.21* 10⁸ m/s.
E) ~7.80 * 10³ m/s.

Question 47

Geosynchronous satellites are such that have the period of rotation about a planet equal to time it takes the planet to rotate about its axis. If such satellite was to be placed to orbit around Venus M_V = 4.867 *10²⁴ kg, R_V = 6.05 *10⁶ m, d_V = 116.75 day), QUOTE what would be its speed?

A) 366 m/s
B) 7.32 km/s
C) 25.9 km/s
D) 8.87 m/s
E) 587 m/s

Question 48

84 * 10⁵ km. A communications satellite is placed in an Earth orbit at 4.23 *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 49

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 50

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

A) 5 * 10⁷ s
B) 2 * 10⁸ s
C) 0.35 * 10⁸ s
D) 2.8 * 10⁸ s
E) 5 * 10⁸ s

Question 51

Five masses orbit around a central mass with central mass M>>m. Which of the orbiting masses will need the highest energy to escape from the orbit?

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

Question 52

If the ratios of masses and radii of Mars to Earth are 0.11 and 0.53, 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 53

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 their centers of masses 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 J

Question 54

On April 12, 1961, Yuri Gagarin became the first man in space when he made his 108-minute trip around the orbit of Earth. What was the height of his orbit relative to Earth's surface? M_E = 5.98 *10²⁴ kg, R_E = 6.37 *10⁶ m)?

A) 1.14 *10⁶ m
B) 4.90 *10⁵ m
C) 2.7 * 10¹² m
D) 6.37 * 10⁶ m
E) 7.51 * 10⁶ m

Question 55

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 56

Two satellites of the same mass are placed in orbits around Earth. Satellite One is at an altitude of 1 R_E and Satellite Two is at an altitude of 2 R_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)1/2
B) 2/3
C) 3/2
D)1/4
E) 2

Question 57

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) The potential energy does not depend on the distance between the masses.

Question 58

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 59

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 60

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.

Question 61

A shopper steps on an escalator moving downward at a constant speed toward the bargain basement in a large department store. On his way down, the normal force exerted on him by the step of the escalator is

A) greater than his weight when he is off the escalator.
B) equal to his weight when he is off the escalator.
C) less than his weight when he is off the escalator.
D) dependent on how fast the escalator is moving.
E) unknown; insufficient information is given to answer correctly.

Question 62

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 , , , )?

A) 0.51
B) 2.0
C) 6.6
D) 5.7
E) 2.5

Question 63

You are going up in an elevator that is accelerating upward on Earth and your apparent weight is measured to be 120% of your weight on Earth. Suppose you were to go in an elevator with the same acceleration on Mars, where acceleration due to gravity is 3.71 m/s². What will be your apparent weight comparing to your weight on Earth?

A) 37.1%
B) 100%
C) 120%
D) 57.8%
E) 44.5%

Question 64

The weight of an object is

A) the same as the mass of the object.
B) the quantity of matter in the object.
C) the mass of the object multiplied by the acceleration due to gravity at sea level, regardless of where the object is located.
D) the result of the gravitational force acting on the object.
E) the reading on a spring scale attached to the object.

Question 65

You are going up in an elevator that is accelerating upward on Earth. Suppose you were to go in an elevator with the same acceleration on Mars. How would your apparent weight on Mars compare to your apparent weight on Earth?

A) It would be smaller.
B) It would be larger.
C) It would be exactly the same, non-zero value.
D) It would be zero.
E) It would depend on my mass.

Question 66

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 67

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 x 10⁶ m, M_E = 5.98 x10²⁴ kg, G = 6.67 x10^-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) 9.68 km/s

Question 68

A body is sent out in space. Which of the following statements is true of this body as it moves away from Earth?

A) The body's mass and weight remain equal.
B) The body's mass remains constant, and its weight decreases.
C) The body's mass decreases, and its weight remains constant.
D) The body's mass and weight decrease.
E) The body's mass decreases, and its weight increases.

Question 69

The radius of the orbit of Earth around the Sun is 150 * 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 70

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 x 10⁶ m, M_E = 5.98 x10²⁴ kg, G = 6.67 x10^-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 71

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 72

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 x10²² kg, R_moon = 1.74 x 10⁶ m, and G = 6.67 x 10^-11 N · m²/kg²)?

A) 3.22 x10⁵ m
B) 1.04 x10¹¹ m
C) 5.67 x10² m
D) 2.53 x10³ m
E) 2.06 x10⁶ m

Question 73

A person of weight w is in an upward-moving elevator when the cable suddenly breaks. What is the person's apparent weight immediately after the elevator starts to fall?

A) w
B) greater than w
C) less than w
D) infinite
E) zero

Question 74

What is the weight of a 50-kg boy on the Moon, where the acceleration due to gravity is 1.6 m/s²?

A) 80 N
B) 100 N
C) 490 N
D) 50 N
E) 80 lb

Question 75

The acceleration due to gravity on the Moon is only about 1/6 of that on Earth. An astronaut whose weight on Earth is 600 N travels to the lunar surface. His mass as measured on the Moon is

A) 600 kg.
B) 100 kg.
C) 61.2 kg.
D) 10.0 kg.
E) 360 kg.

Question 76

An astronaut lands on an Earthlike planet and drops a small lead ball with a mass of 76.5 g from the top of her spaceship. The point of release is 18 m above the surface of the planet and the ball takes 2.5 s to reach the ground. The astronaut's mass on Earth is 68.5 kg. Her weight on the planet is

A) 69.0 N.
B) 395 N.
C) 670 N.
D) 990 N.
E) 1.02 kN.

Question 77

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

A) 8.31 * 10¹ m/s
B) 6.90 * 10³ m/s
C) 4.76 *10⁷ m/s
D) 9.62 * 10⁴ m/s
E) 1.41× 10⁴ m/s

Question 78

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 * 10⁶ km).

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

Question 79

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 x 10⁶ m, M_E = 5.98 x 10²⁴ kg, G = 6.67 x 10^-11 N · m²/kg²). Assume the satellite is stationary on Earth's surface and is moving with appropriate speed on the orbit.

A) 3.13 x 10¹⁰ J
B) 8.34 x 10¹⁰ J
C) 4.69 x 10¹⁰ J
D) 6.25 x 10¹⁰ J
E) 1.56 x 10¹⁰ J

Question 80

Suppose that a satellite is in a circular orbit at a height of 2.00 x10⁶ 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) 0.248 h