# Quiz 13: Newtons Theory of Gravity

Physics & Astronomy

Q 1Q 1

A baseball is located at the surface of the earth. Which statements about it are correct? (There may be more than one correct choice.)
A) The earth exerts a much greater gravitational force on the ball than the ball exerts on the earth.
B) The ball exerts a greater gravitational force on the earth than the earth exerts on the ball.
C) The gravitational force on the ball due to the earth is exactly the same as the gravitational force on the earth due to the ball.
D) The gravitational force on the ball is independent of the mass of the ball.
E) The gravitational force on the ball is independent of the mass of the earth.

Free

Multiple Choice

C

Q 2Q 2

A very small round ball is located near a large solid sphere of uniform density. The force that the large sphere exerts on the ball
A) is exactly the same as it would be if all the mass of the sphere were concentrated at the center of the sphere.
B) is approximately the same as it would be if all the mass of the sphere were concentrated at the center of the sphere.
C) is independent of the mass of the ball.
D) is independent of the mass of the sphere.
E) can only be calculated using calculus.

Free

Multiple Choice

A

Q 3Q 3

Planet Z-34 has a mass equal to 1/3 that of Earth, a radius equal to 1/3 that of Earth, and an axial spin rate 1/2 that of Earth. With g representing, as usual, the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the surface of Z-34 is
A) g/3.
B) 3g.
C) 6g.
D) g/9.
E) 9g.

Free

Multiple Choice

B

Q 4Q 4

If the mass of the earth and all objects on it were suddenly doubled, but the size remained the same, the acceleration due to gravity at the surface would become
A) 4 times what it now is.
B) 2 times what it now is.
C) the same as it now is.
D) 1/2 of what it now is.
E) 1/4 of what it now is.

Free

Multiple Choice

Q 5Q 5

Two planets having equal masses are in circular orbit around a star. Planet A has a smaller orbital radius than planet B. Which statement is true?
A) Planet A has more kinetic energy, less potential energy, and less mechanical energy (potential plus kinetic) than planet B.
B) Planet A has more kinetic energy, more potential energy, and more mechanical energy (potential plus kinetic) than planet B.
C) Planet A has more kinetic energy, less potential energy, and more mechanical energy (potential plus kinetic) than planet B.
D) Planet A and planet B have the same amount of mechanical energy (potential plus kinetic).

Free

Multiple Choice

Q 6Q 6

A certain planet has an escape speed V. If another planet of the same size has twice the mass as the first planet, its escape speed will be
A) 2V.
B) V.
C) V.
D) V/2.
E) V/ .

Free

Multiple Choice

Q 7Q 7

A certain planet has an escape speed V. If another planet has twice size and twice the mass of the first planet, its escape speed will be
A) 2V.
B) V.
C) V.
D) V/2.
E) V/ .

Free

Multiple Choice

Q 8Q 8

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

Free

True False

Q 9Q 9

A satellite in a circular orbit of radius R around planet X has an orbital period T. If Planet X had one-fourth as much mass, the orbital period of this satellite in an orbit of the same radius would be
A) 4T.
B) 2T.
C) T
D) T/2.
E) T/4.

Free

Multiple Choice

Q 10Q 10

A satellite of mass m has an orbital period T when it is in a circular orbit of radius R around the earth. If the satellite instead had mass 4m, its orbital period would be
A) 4T.
B) 2T.
C) T.
D) T/2.
E) T/4.

Free

Multiple Choice

Q 11Q 11

The reason an astronaut in an earth satellite feels weightless is that
A) the astronaut is beyond the range of the earth's gravity.
B) the astronaut is falling.
C) the astronaut is at a point in space where the effects of the moon's gravity and the earth's gravity cancel.
D) this is a psychological effect associated with rapid motion.
E) the astronaut's acceleration is zero.

Free

Multiple Choice

Q 12Q 12

Because the earth's orbit is slightly elliptical, the earth actually gets closer to the sun during part of the year. When the earth is closer to the sun its orbital speed is
A) less than when the earth is farthest away from the sun.
B) the same as when the earth is farthest away from the sun.
C) greater than when the earth is farthest away from the sun.

Free

Multiple Choice

Q 13Q 13

A small-sized 155-kg mass is located 1.50 m from a small-sized 275-kg mass, with both masses fixed in place. Where should you place a third small-sized mass so that the net gravitational force on it due to the original two masses is zero?

Free

Essay

Q 14Q 14

An astronaut is in equilibrium when he is positioned 140 km from the center of asteroid X and 581 km from the center of asteroid Y, along the straight line joining the centers of the asteroids. What is the ratio of the masses X/Y of the asteroids?
A) 0.0581
B) 17.2
C) 0.241
D) 4.15

Free

Multiple Choice

Q 15Q 15

Three identical very small 50-kg masses are held at the corners of an equilateral triangle, 0.30 m on each side. If one of the masses is released, what is its initial acceleration if the only forces acting on it are the gravitational forces due to the other two masses? (G = 6.67 × 10

^{-11}N ∙ m^{2}/kg^{2}) A) 3.7 × 10^{-8 }m/s^{2}B) 2.5 × 10^{-8 }m/s^{2}C) 1.9 × 10^{-8 }m/s^{2}D) 4.2 × 10^{-8 }m/s^{2}E) 6.4 × 10^{-8 }m/s^{2}Free

Multiple Choice

Q 16Q 16

A small planet having a radius of 1000 km exerts a gravitational force of 100 N on an object that is 500 km above its surface. If this object is moved 500 km farther from the planet, the gravitational force on it will be closest to
A) 75 N.
B) 71 N.
C) 56 N.
D) 50 N.
E) 25 N.

Free

Multiple Choice

Q 17Q 17

The gravitational acceleration on a planet's surface is 16.0 m/s

^{2}. What is the gravitational acceleration at an altitude of one planet diameter above the SURFACE of the planet? A) 5.33 m/s^{2}B) 1.78 m/s^{2}C) 1.60 m/s^{2}D) 4.00 m/s^{2}E) 8.00 m/s^{2}Free

Multiple Choice

Q 18Q 18

The radius of the earth is R. At what distance above the earth's surface will the acceleration of gravity be 4.9 m/s

^{2}? A) 0.41R B) 0.50R C) 1.0R D) 1.4R E) 2.0RFree

Multiple Choice

Q 19Q 19

By how many newtons does the weight of a 100-kg person change when he goes from sea level to an altitude of 5.0 km if we neglect the earth's rotational effects? (The mean radius of the Earth is 6.38 × 10

^{6}m, G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}.) A) -0.60 N B) -1.5 N C) -2.6 N D) -3.6 N E) -5.2 NFree

Multiple Choice

Q 20Q 20

The weight of spaceman Speff at the surface of planet X, solely due to its gravitational pull, is 389 N. If he moves to a distance of 1.86 × 10

^{4}km above the planet's surface, his weight changes to 24.31 N. What is the mass of planet X, if Speff's mass is 75.0 kg? (G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}) A) 2.99 × 10^{24}kg B) 2.99 × 10^{18}kg C) 2.99 × 10^{17}kg D) 1.59 × 10^{18}kgFree

Multiple Choice

Q 21Q 21

From what height above the surface of the earth should an object be dropped to initially experience an acceleration of 0.9200g? The radius of the earth is 6.38 × 10

^{6}m. A) 272 km B) 260 km C) 554 km D) 510 kmFree

Multiple Choice

Q 22Q 22

An object drops a distance h in a time of 6.3 s on the surface of the earth (neglecting air effects). How long would it take the same object to drop the same distance on the surface of spherical asteroid X having a mass of 1.1 × 10

^{22}kg and a radius of 4.0 × 10^{5}m? (G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}, M_{earth}= 5.97 × 10^{24}kg, R_{earth}= 6.38 × 10^{6}m) A) 9.2 s B) 6.3 s C) 5.2 s D) 12 s E) 3.3 sFree

Multiple Choice

Q 23Q 23

Ekapluto is an unknown planet that has two spherical moons in circular orbits. The table summarizes the hypothetical data about the moons. Both moons have low axial spin rates. (G = 6.67 × 10

^{-11}N ∙ m^{2}/kg^{2}) The acceleration due to gravity at the surface of Moon B is A) 0.10 m/s^{2}. B) 0.15 m/s^{2}. C) 0.20 m/s^{2}. D) 0.25 m/s^{2}. E) 0.30 m/s^{2}.Free

Multiple Choice

Q 24Q 24

Sputnik I was launched into orbit around Earth in 1957. It had a perigee (the closest approach to Earth, measured from Earth's center) of 6.81 × 10

^{6}m and an apogee (the furthest point from Earth's center) of 7.53 × 10^{6}m. What was its speed when it was at its perigee? The mass of Earth is 5.97 × 10^{24}kg and G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}. A) 7180 m/s B) 7840 m/s C) 8230 m/s D) 11,000 m/s E) 13,400 m/sFree

Multiple Choice

Q 25Q 25

Beings on spherical asteroid Π have observed that a large rock is approaching their asteroid in a collision course. At 7514 km from the center of the asteroid, the rock has a speed of 136.0 m/s and later at 2823 km it has a speed of 392.0 m/s. Use energy conservation to find the mass of asteroid Π. You can neglect any effects due to the parent star of the asteroid. (G = 6.67 × 10

^{-11}N ∙ m^{2}/kg^{2}) A) 4.582 × 10^{21}kg B) 9.164 × 10^{27}kg C) 6.112 × 10^{28}kg D) 4.582 × 10^{20}kgFree

Multiple Choice

Q 26Q 26

What is the ratio of the escape speed of a rocket launched from sea level to the escape speed of one launched from Mt. Everest (an altitude of 8.85 km)? The radius of the earth is 6.38 × 10

^{6}m. A) 1.0007 B) 1.0014 C) 1.0001 D) 0.9986 E) 0.9993Free

Multiple Choice

Q 27Q 27

A huge cannon is assembled on an airless planet having insignificant axial spin. The planet has a radius of 5.00 × 10

^{6}m and a mass of 3.95 × 10^{23}kg. The cannon fires a projectile straight up at 2000 m/s. An observation satellite orbits the planet at a height of 1000 km. What is the projectile's speed as it passes the satellite? (G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}) A) 1500 m/s B) 1380 m/s C) 1610 m/s D) 1280 m/sFree

Multiple Choice

Q 28Q 28

A meteoroid, heading straight for Earth, has a speed of 14.8 km/s relative to the center of Earth as it crosses our moon's orbit, a distance of 3.84 × 10

^{8}m from the earth's center. What is the meteroid's speed as it hits the earth? You can neglect the effects of the moon, Earth's atmosphere, and any motion of the earth. (G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}, M_{earth}= 5.97 × 10^{24}kg) A) 18.5 km/s B) 21.5 km/s C) 32.4 km/s D) 87.3 km/sFree

Multiple Choice

Q 29Q 29

A certain spherical asteroid has a mass of 3.5 × 10

^{16}kg and a radius of 8.8 km. What is the minimum speed needed to escape from the surface of this asteroid? (G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}) A) 23 m/s B) 16 m/s C) 520 m/s D) 730 m/sFree

Multiple Choice

Q 30Q 30

A 910-kg object is released from rest at an altitude of 1200 km above the north pole of the earth. If we ignore atmospheric friction, with what speed does the object strike the surface of the earth? (G = 6.67 × 10

^{-11}N ∙ m^{2}/kg^{2}, M_{earth}= 5.97 × 10^{24}kg, the polar radius of the earth is 6357 km) A) 4.5 km/s B) 2.2 km/s C) 2.7 km/s D) 3.2 km/s E) 4.8 km/sFree

Multiple Choice

Q 31Q 31

A satellite is in circular orbit at an altitude of 1500 km above the surface of a nonrotating planet with an orbital speed of 9.2 km/s. The minimum speed needed to escape from the surface of the planet is 14.9 km/s, and G = 6.67 × 10

^{-11}N ∙ m^{2}/kg^{2}. The orbital period of the satellite is closest to A) 72 min. B) 65 min. C) 58 min. D) 51 min. E) 44 min.Free

Multiple Choice

Q 32Q 32

A satellite is in circular orbit at an altitude of 2300 km above the surface of a nonrotating asteroid with an orbital speed of 5.9 km/s. The minimum speed needed to escape from the surface of the asteroid is 14.6 km/s, and G = 6.67 × 10

^{-11}N ∙ m^{2}/kg^{2}. The mass of the asteroid is closest to A) 1.8 × 10^{24}_{ }_{kg.}B) 8.9 × 10^{23}_{ }_{kg.}C) 1.3 × 10^{24}_{ }_{kg.}D) 2.7 × 10^{24}_{ kg.}E) 3.6 × 10^{24}_{ }_{kg.}Free

Multiple Choice

Q 33Q 33

An astronaut is standing on the surface of a planetary satellite that has a radius of 1.74 × 10

^{6}m and a mass of 7.35 × 10^{22}kg. An experiment is planned where a projectile needs to be launched straight up from the surface. What must be the minimum initial speed of the projectile so it will reach a height of 2.55 × 10^{6}m above this satellite's surface? (G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2})Free

Short Answer

Q 34Q 34

The International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is 5.97 × 10

^{24}kg, the radius of the earth is 6.38 × 10^{6}m, and G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}. Assuming a circular orbit, (a) what is the period of the International Space Station's orbit? (b) what is the speed of the International Space Station in its orbit?Free

Essay

Q 35Q 35

A satellite that weighs 4900 N on the launchpad travels around the earth's equator in a circular orbit with a period of 1.667 h. The earth's mass is 5.97 × 10

^{24}kg, its equatorial radius is 6.3 × 10^{6}m, and G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}. (a) Calculate the magnitude of the earth's gravitational force on the satellite. (b) Determine the altitude of the satellite above the Earth's SURFACE.Free

Essay

Q 36Q 36

What is the period (in hours) of a satellite circling Mars 100 km above the planet's surface? The mass of Mars is 6.42 × 10

^{23}kg, its radius is 3.40 × 10^{6}m, and G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}. A) 1.75 h B) 1.25 h C) 1.15 h D) 1.00 h E) 1.45 hFree

Multiple Choice

Q 37Q 37

Jupiter completes one revolution about its own axis every 9.92 hours. What is the radius of the orbit required for a satellite to revolve about Jupiter with the same period? Jupiter has a mass of 1.90 × 10

^{27}kg and G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}. A) 1.04 × 10^{7}m B) 2.26 × 10^{9}m C) 1.60 × 10^{8}m D) 3.41 × 10^{8}m E) 7.45 × 10^{8}mFree

Multiple Choice

Q 38Q 38

The moons of Mars, Phobos (Fear) and Deimos (Terror), are very close to the planet compared to Earth's Moon. Their orbital radii are 9,378 km and 23,459 km respectively. What is the ratio of the orbital speed of Phobos to that of Deimos?
A) 0.2528
B) 0.3998
C) 1.582
D) 2.858
E) 3.956

Free

Multiple Choice

Q 39Q 39

Spaceman Speff orbits spherical asteroid X with his spaceship. To remain in a circular orbit at
421 km from the asteroid's center, he should maintain a speed of
What is the mass of planet X? (G = 6.67 × 10

^{-11}N ∙ m^{2}/kg^{2}) A) 4.0 × 10^{19}kg B) 5.1 × 10^{17}kg C) 4.0 × 10^{16}kg D) 5.1 × 10^{14}kgFree

Multiple Choice

Q 40Q 40

Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is 5.68 × 10

^{26}kg and the rings have an average radius of 100,000 km. (G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}) A) 19.5 km/s B) 27.5 km/s C) 13.8 km/s D) 1.95 km/sFree

Multiple Choice

Q 41Q 41

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 × 10

^{7}m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 1.8 × 10^{11}m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 59.7 m/s^{2}. What are the mass of (a) the planet and (b) the star? (G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}.) A) (a) 7.2 kg × 10^{25}kg, (b) 2.9 kg × 10^{30}kg B) (a) 1.3 kg × 10^{26}kg, (b) 2.9 kg × 10^{30}kg C) (a) 7.2 kg × 10^{25}kg, (b) 1.7 kg × 10^{30}kg D) (a) 1.3 kg × 10^{26}kg, (b) 1.7 kg × 10^{30}kgFree

Multiple Choice

Q 42Q 42

Suppose we want a satellite to revolve around the earth 5 times a day. What should be the radius of its orbit? (The mass of the earth is 5.97 × 10

^{24}kg, G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2}, and you can neglect the presence of the moon.) A) 1.44 × 10^{7}m B) 0.690 × 10^{7}m C) 7.22 × 10^{7}m D) 2.11 × 10^{7}mFree

Multiple Choice

Q 43Q 43

Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. (G = 6.67 × 10

^{-11}N ∙ m^{2}/kg^{2}) The mass of Ekapluto is closest to A) 1.0 × 10^{22}kg. B) 3.0 × 10^{22}kg. C) 1.0 × 10^{23}kg. D) 3.0 × 10^{23}kg. E) 1.0 × 10^{24}kg.Free

Multiple Choice

Q 44Q 44

A man-made satellite of mass 6105 kg is in orbit around the earth, making one revolution in 430 minutes. What is the magnitude of the gravitational force exerted on the satellite by the earth? (The mass of the earth is 6.0 × 10

^{24}kg and G = 6.67 × 10^{-11}N ∙ m^{2}/kg^{2})Free

Short Answer

Q 45Q 45

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 10

^{7}m. The second planet has an orbital radius 3.00 × 10^{7}m. What is the period of the second satellite? A) 60.8 h B) 12.0 h C) 33.1 h D) 9.80 h E) 27.0 hFree

Multiple Choice

Q 46Q 46

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 10

^{7}m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite? A) 4.50 × 10^{7}B) 3.90 × 10^{7}C) 9.24 × 10^{7}D) 8.00 × 10^{7}E) 7.27 × 10^{7}Free

Multiple Choice

Q 47Q 47

Neptune circles the Sun at a distance of 4.50 × 10

^{12}m once every 164 years. Saturn circles the Sun at a distance of 1.43 x 10^{12}m. What is the orbital period of Saturn? A) 304 y B) 121 y C) 109 h D) 88.6 y E) 29.4 yFree

Multiple Choice

Q 48Q 48

The moons of Mars, Phobos (Fear) and Deimos (Terror), are very close to the planet compared to Earth's Moon. Their orbital radii are 9,378 km and 23,459 km respectively. What is the ratio of the period of revolution of Phobos to that of Deimos?
A) 0.2528
B) 0.3998
C) 1.582
D) 2.858
E) 3.956

Free

Multiple Choice

Q 49Q 49

Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?
A) 20 d
B) 40 d
C) 80 d
D) 160 d
E) 320 d

Free

Multiple Choice

Q 50Q 50

Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. The orbital period of Moon B is closest to
A) 5.6 × 10

^{6}s. B) 6.0 × 10^{6}s. C) 6.4 × 10^{6}s. D) 6.9 × 10^{6}s. E) 7.3 × 10^{6}s.Free

Multiple Choice