# Quiz 13: Gravitation

Physics & Astronomy

Q 1Q 1

In the formula F = Gm

_{1}m_{2}/r^{2}, the quantity G: A)depends on the local value of g B)is used only when the Earth is one of the two masses C)is greatest at the surface of the Earth D)is a universal constant of nature E)is related to the Sun in the same way that g is related to the EarthFree

Multiple Choice

D

Q 2Q 2

Suitable units for the gravitational constant G are:
A)kgm/s

^{2}B)m/s^{2}C)Ns/m D)kgm/s E)m^{3}/(kgs^{2})Free

Multiple Choice

E

Q 3Q 3

The gravitational constant G has the derived units
A)Nm
B)Nm/kg
C)Nkg/m
D)Nm

^{2}/kg^{2}E)Nkg^{2}/m^{2}Free

Multiple Choice

D

Q 4Q 4

The mass of an object:
A)is slightly different at different locations on the Earth
B)is a vector
C)is independent of the acceleration due to gravity
D)is the same for all objects of the same size and shape
E)can be measured directly and accurately on a spring scale

Free

Multiple Choice

Q 5Q 5

The magnitude of the acceleration of a planet in orbit around the Sun is proportional to:
A)the mass of the planet
B)the mass of the Sun
C)the distance between the planet and the Sun
D)the reciprocal of the distance between the planet and the Sun
E)the product of the mass of the planet and the mass of the Sun

Free

Multiple Choice

Q 6Q 6

Earth exerts a gravitational force on the Moon, keeping it in its orbit.The reaction to this force, in the sense of Newton's third law, is:
A)the centripetal force on the Moon
B)the nearly circular orbit of the Moon
C)the gravitational force exerted on Earth by the Moon
D)the tides due to the Moon
E)the apple hitting Newton on the head

Free

Multiple Choice

Q 7Q 7

Let F

_{1}be the magnitude of the gravitational force exerted on the Sun by Earth and F_{2}be the magnitude of the force exerted on Earth by the Sun.Then: A)F_{1}is much greater than F_{2}B)F_{1}is slightly greater than F_{2}C)F_{1}is equal to F_{2}D)F_{1}is slightly less than F_{2}E)F_{1}is much less than F_{2}Free

Multiple Choice

Q 8Q 8

An astronaut on the Moon simultaneously drops a feather and a hammer.The fact that they land together shows that:
A)no gravity forces act on a body in a vacuum
B)the acceleration due to gravity on the Moon is less than g on the Earth
C)in the absence of air resistance all bodies at a given location fall with the same acceleration
D)the feather has a greater weight on the Moon than on Earth
E)G = 0 on the Moon

Free

Multiple Choice

Q 9Q 9

Three particles, two with mass m and one mass M, might be arranged in any of the four configurations known below.Rank the configurations according to the magnitude of the gravitational force on M, least to greatest.
A)1, 2, 3, 4
B)2, 1, 3, 4
C)2, 1, 4, 3
D)2, 3, 4, 2
E)2, 3, 2, 4

Free

Multiple Choice

Q 10Q 10

Four particles, each with mass m, are arranged symmetrically about the origin on the x axis.A fifth particle, with mass M, is on the y axis.The direction of the gravitational force on M is:
A)
B)
C)
D)
E)none of these directions

Free

Multiple Choice

Q 11Q 11

Let M denote the mass of Earth and let R denote its radius.The ratio g/G at Earth's surface is:
A)R

^{2}/M B)M/R^{2}C)MR^{2}D)M/R E)R/MFree

Multiple Choice

Q 12Q 12

An object at the surface of Earth (at a distance R from the center of Earth)weighs 90 N.Its weight at a distance 3R from the center of Earth is:
A)10 N
B)30 N
C)90 N
D)270 N
E)810 N

Free

Multiple Choice

Q 13Q 13

An object is raised from the surface of Earth to a height of two Earth radii above Earth.Then:
A)its mass increases and its weight remains constant
B)both its mass and weight remain constant
C)its mass remains constant and its weight decreases
D)both its mass and its weight decrease
E)its mass remains constant and its weight increases

Free

Multiple Choice

Q 14Q 14

The approximate value of g at an altitude above Earth equal to one Earth diameter is:
A)9.8 m/s

^{2}B)4.9 m/s^{2}C)2.5 m/s^{2}D)1.9 m/s^{2}E)1.1 m/s^{2}Free

Multiple Choice

Q 15Q 15

An artificial satellite of the Earth releases a bomb.Neglecting air resistance, the bomb will:
A)strike Earth under the satellite at the instant of release
B)strike Earth under the satellite at the instant of impact
C)strike Earth ahead of the satellite at the instant of impact
D)strike Earth behind the satellite at the instant of impact
E)never strike Earth

Free

Multiple Choice

Q 16Q 16

An astronaut finishes some work on the outside of his satellite, which is in circular orbit around the Earth.He leaves his wrench outside the satellite.If there is no air resistance, the wrench will:
A)fall directly down to the Earth
B)continue in orbit at reduced speed
C)continue in orbit with the satellite
D)fly off tangentially into space
E)spiral down to the Earth

Free

Multiple Choice

Q 17Q 17

Suppose you have a pendulum clock which keeps correct time on Earth (acceleration due to gravity = 9.8 m/s

^{2}).Without changing the clock, you take it to the Moon (acceleration due to gravity = 1.6 m/s^{2}).For every hour interval (on Earth)the Moon clock will record: A)(9.8/1.6)h B)1 h C)h D)(1.6/9.8)h E)hFree

Multiple Choice

Q 18Q 18

If Earth were to rotate only 100 times per year about its axis:
A)airplanes flying west to east would make better time
B)we would fly off Earth's surface
C)our apparent weight would slightly increase
D)Earth's atmosphere would float into outer space
E)our apparent weight would slightly decrease

Free

Multiple Choice

Q 19Q 19

Mars has a mass of about 0.1075 times the mass of Earth and a diameter of about 0.533 times the diameter of Earth.The acceleration of a body falling near the surface of Mars is about:
A)0.30 m/s

^{2}B)1.4 m/s^{2}C)2.0 m/s^{2}D)3.7 m/s^{2}E)26 m/s^{2}Free

Multiple Choice

Q 20Q 20

The mass of a hypothetical planet is 1/100 that of Earth and its radius is 1/4 that of Earth.If a person weighs 600 N on Earth, what would he weigh on this planet?
A)24 N
B)48 N
C)96 N
D)192 N
E)600 N

Free

Multiple Choice

Q 21Q 21

A rocket ship is coasting toward a planet.Its captain wishes to know the value of g at the surface of the planet.This may be inferred by:
A)measuring the apparent weight of one of the crew
B)measuring the apparent weight of an object of known mass in the ship
C)measuring the diameter of the planet
D)measuring the density of the planet
E)observing the ship's acceleration and correcting for the distance from the center of the planet

Free

Multiple Choice

Q 22Q 22

An astronaut in an orbiting space-craft feels "weightless" because she:
A)is beyond the range of gravity
B)is pulled outwards by centrifugal force
C)has no acceleration
D)has the same acceleration as the space-craft
E)is outside Earth's atmosphere

Free

Multiple Choice

Q 23Q 23

A particle might be placed Rank these situations according to the magnitude of the gravitational force on the particle, least to greatest.
A)All tie
B)1, 2, 3, 4
C)1 and 2 tie, then 3 and 4 tie
D)1 and 2 tie, then 3, then 4
E)1 and 2 tie, then 4, then 3

Free

Multiple Choice

Q 24Q 24

A spring scale, calibrated in newtons, is used to weigh sugar.If it were possible to weigh sugar at the following locations, where will the buyer get the most sugar to a newton?
A)At the north pole
B)At the equator
C)Near the center of Earth
D)On the Moon
E)On Jupiter

Free

Multiple Choice

Q 25Q 25

Of the following where would the weight of an object be the least?
A)2000 miles above Earth's surface
B)At the north pole
C)At the equator
D)At the center of Earth
E)At the south pole

Free

Multiple Choice

Q 26Q 26

The mass density of a certain planet has spherical symmetry but varies in such a way that the mass inside every spherical surface with center at the center of the planet is proportional to the radius of the surface.If r is the distance from the center of the planet to a point mass inside the planet, the gravitational force on the mass is:
A)not dependent on r
B)proportional to r

^{2}C)proportional to r D)proportional to 1/r E)proportional to 1/r^{2}Free

Multiple Choice

Q 27Q 27

Two particles, each of mass m, are a distance d apart.To bring a third particle, with mass 2m, from far away to a resting point midway between the two particles, an external agent must do work equal to:
A)4Gm

^{2}/d B)-4Gm^{2}/d C)8Gm^{2}/d D)-8Gm^{2}/d E)zeroFree

Multiple Choice

Q 28Q 28

An artificial Earth satellite is moved from a circular orbit with radius R to a circular orbit with radius 2R.During this move:
A)The gravitational force does no work.
B)The gravitational force does positive work.
C)The gravitational force does negative work.
D)The work done by the gravitational force cannot be determined without knowing the path of the satellite.
E)The work done by the gravitational force cannot be determined without knowing what force caused the satellite to change its orbit.

Free

Multiple Choice

Q 29Q 29

An artificial Earth satellite of mass m is moved from a circular orbit with radius R to a circular orbit with radius 2R.If the mass of the Earth is M

_{E}, the work done by the gravitational force is: A)zero B)GM_{E}m/R C)GM_{E}m/2R D)−GM_{E}m/R E)−GM_{E}m/2RFree

Multiple Choice

Q 30Q 30

A projectile is fired straight upward from Earth's surface with a speed that is half the escape speed.If R is the radius of Earth, the highest altitude reached, measured from the surface, is:
A)R/4
B)R/3
C)R/2
D)R
E)2R

Free

Multiple Choice

Q 31Q 31

To measure the mass of a planet with the same radius as Earth, an astronaut drops an object from rest (relative to the planet)from an altitude of one radius above the surface.When the object hits its speed is 4 times what it would be if the same experiment were carried out for Earth.In units of M

_{E}(the mass of the Earth), the mass of the planet is: A)2 M_{E}B)4 M_{E}C)8 M_{E}D)16 M_{E}E)32 M_{E}Free

Multiple Choice

Q 32Q 32

In order to fire a projectile upward and have it escape the Earth's gravity,
A)the kinetic energy of the projectile may have any positive value.
B)the potential energy of the projectile must be positive
C)the total energy (kinetic plus potential)of the projectile must be negative
D)the total energy (kinetic plus potential)of the projectile must not be negative
E)the total energy (kinetic plus potential)of the projectile must be exactly zero

Free

Multiple Choice

Q 33Q 33

The escape velocity at the surface of Earth is approximately 11 km/s.What is the mass, in units of M

_{E}(the mass of the Earth), of a planet with twice the radius of Earth for which the escape speed is twice that for Earth? A)2 M_{E}B)4 M_{E}C)8 M_{E}D)1/2 M_{E}E)1/4 M_{E}Free

Multiple Choice

Q 34Q 34

Neglecting air resistance, a 1.0-kg projectile has an escape velocity of about 11 km/s at the surface of Earth.The corresponding escape velocity for a 2.0 kg projectile is:
A)5.5 km/s
B)7.8 km/s
C)11 km/s
D)16 km/s
E)22 km/s

Free

Multiple Choice

Q 35Q 35

Neglecting air resistance, the escape speed from a certain planet for an empty space vehicle is 1.12 10

^{4}m/s.What is the corresponding escape speed for the fully loaded vehicle which has triple the mass of the empty one? A)3.73 10^{3}m/s B)1.12 10^{4}m/s C)3.36 10^{4}m/s D)1.01 10^{5}m/s E)1.40 10^{12}m/sFree

Multiple Choice

Q 36Q 36

Consider the statement: "Earth moves in a stable orbit around the Sun and is therefore in equilibrium".The statement is:
A)false, because no moving body can be in equilibrium
B)true, because the Earth does not fall into or fly away from the sun
C)false, because the Earth is rotating on its axis and no rotating body can be in equilibrium
D)false, because the Earth has a considerable acceleration
E)true, because if it were not in equilibrium then buildings and structures would not be stable

Free

Multiple Choice

Q 37Q 37

A planet travels in an elliptical orbit about a star X as shown.The magnitude of the acceleration of the planet is:
A)greatest at point Q
B)greatest at point S
C)greatest at point U
D)greatest at point W
E)the same at all points

Free

Multiple Choice

Q 38Q 38

The speed of a comet in an elliptical orbit about the sun:
A)decreases while it is receding from the sun
B)is constant
C)is greatest when farthest from the sun
D)varies sinusoidally with time
E)equals L/(mr), where L is its angular momentum, m is its mass, and r is its distance from the sun

Free

Multiple Choice

Q 39Q 39

A planet travels in an elliptical orbit about a star as shown.At what pair of points is the speed of the planet the same?
A)W and S
B)P and T
C)P and R
D)Q and U
E)Vand R

Free

Multiple Choice

Q 40Q 40

For a planet in orbit around a star the perihelion distance is r

_{p}and its speed at perihelion is v_{p}.The aphelion distance is r_{a}and its speed at aphelion is v_{a}.Which of following is true? A)v_{a}= v_{p}B)v_{a}/r_{a}= v_{p}/r_{p}C)v_{a}r_{a}= v_{p }r_{p}D)v_{a/}r_{a}^{ 2}= v_{p/}r_{p}^{ 2}E)v_{a}r_{a}^{ 2}= v_{p }r_{p}^{ 2}Free

Multiple Choice

Q 41Q 41

A small satellite is in elliptical orbit around Earth as shown.If L denotes the magnitude of its angular momentum and K denotes kinetic energy:
A)L

_{2}> L_{1}and K_{2}> K_{1}B)L_{2}> L_{1}and K_{2}= K_{1}C)L_{2}= L_{1}and K_{2}= K_{1}D)L_{2}< L_{1}and K_{2}= K_{1}E)L_{2}= L_{1}and K_{2}> K_{1}Free

Multiple Choice

Q 42Q 42

In planetary motion the line from the star to the planet sweeps out equal areas in equal times.This is a direct consequence of:
A)the conservation of energy
B)the conservation of momentum
C)the conservation of angular momentum
D)the conservation of mass
E)none of the above

Free

Multiple Choice

Q 43Q 43

The elliptical orbit of a planet around the Sun is shown on the diagram.Which of the following statements is true?
A)the eccentricity of the orbit is less than zero
B)the eccentricity of the orbit is greater than 1
C)the sun might be at point C
D)the sun might be at point D
E)the sun might be at point B

Free

Multiple Choice

Q 44Q 44

The orbit of a certain a satellite has a semimajor axis of 1.5 10

^{7}m and an eccentricity of 0.20.Its perigee (minimum distance)and apogee (maximum distance)are respectively: A)1.2 10^{7}m, 1.8 10^{7}m B)3.0 10^{6}m, 1.2 10^{7}m C)6.0 10^{6}m, 9.0 10^{6}m D)1.0 10^{7}m, 1.2 10^{7}m E)9.6 10^{6}m, 1.8 10^{7}mFree

Multiple Choice

Q 45Q 45

Planet 1 and planet 2 are both in circular orbits around the same central star.The orbit of planet 2 has a radius that is much larger than the radius of the orbit of planet 1.This means that:
A)the period of planet 1 is greater than the period of planet 2 and the speed of planet 1 is greater than the speed of planet 2
B)the period of planet 1 is greater than the period of planet 2 and the speed of planet 1 is less than the speed of planet 2
C)the period of planet 1 is less than the period of planet 2 and the speed of planet 1 is less than the speed of planet 2
D)the period of planet 1 is less than the period of planet 2 and the speed of planet 1 is greater than the speed of planet 2
E)the planets have the same speed and the same period

Free

Multiple Choice

Q 46Q 46

A planet is in circular orbit around the Sun.Its distance from the Sun is four times the average distance of Earth from the Sun.The period of this planet is:
A)4 Earth years
B)8 Earth years
C)16 Earth years
D)64 Earth years
E)2.5 Earth years

Free

Multiple Choice

Q 47Q 47

Two planets are orbiting a star in a distant galaxy.The first has a semimajor axis of 150 10

^{6}km, an eccentricity of 0.20, and a period of 1.0 Earth years.The second has a semimajor axis of 250 10^{6}km, an eccentricity of 0.30, and a period of: A)0.46 Earth yr B)0.57 Earth yr C)1.4 Earth yr D)1.7 Earth yr E)2.8 Earth yrFree

Multiple Choice

Q 48Q 48

Given the perihelion distance, aphelion distance, and speed at perihelion of a planet, which of the following CANNOT be calculated?
A)the mass of the star
B)the mass of the planet
C)the speed of the planet at aphelion
D)the period of orbit
E)the semimajor axis of the orbit

Free

Multiple Choice

Q 49Q 49

Assume that Earth is in circular orbit around the Sun with kinetic energy K and potential energy U, taken to be zero for infinite separation.Then, the relationship between K and U:
A)is K = U
B)is K = -U
C)is K = U/2
D)is K = -U/2
E)depends on the radius of the orbit

Free

Multiple Choice

Q 50Q 50

An artificial Earth satellite is moved from a circular orbit with radius R to a circular orbit with radius 2R.During this move:
A)the gravitational force does positive work, the kinetic energy of the satellite increases, and the potential energy of the Earth-satellite system increases
B)the gravitational force does positive work, the kinetic energy of the satellite increases, and the potential energy of the Earth-satellite system decreases
C)the gravitational force does positive work, the kinetic energy of the satellite decreases, and the potential energy of the Earth-satellite system increases
D)the gravitational force does negative work, the kinetic energy of the satellite system increases, and the potential energy of the Earth-satellite system decreases
E)the gravitational force does negative work, the kinetic energy of the satellite decreases, and the potential energy of the Earth-satellite system increases

Free

Multiple Choice

Q 51Q 51

An artificial satellite of Earth nears the end of its life due to air resistance.While still in orbit:
A)it moves faster as the orbit lowers
B)it moves slower as the orbit lowers
C)it slowly spirals away from Earth
D)it moves slower in the same orbit but with a decreasing period
E)it moves faster in the same orbit but with an increasing period

Free

Multiple Choice

Q 52Q 52

A planet in another solar system orbits a star with a mass of 4.0 10

^{30}kg.At one point in its orbit it is 250 10^{6}km from the star and is moving at 35 km/s.Take the universal gravitational constant to be 6.67 10^{-11}m^{2}/s^{2} kg and calculate the semimajor axis of the planet's orbit.The result is: A)79 10^{6}km B)140 10^{6}km C)290 10^{6}km D)320 10^{6}km E)590 10^{6}kmFree

Multiple Choice

Q 53Q 53

Einstein's principle of equivalence states:
A)the gravitational constant is the same everywhere in the universe
B)it is impossible to tell the difference between gravitational force and the normal force
C)every mass exerts a gravitational force on every other mass
D)gravitational mass and inertial mass are the same
E)the laws of physics are the same in all inertial reference frames

Free

Multiple Choice

Q 54Q 54

In Einstein's theory of gravitation, gravity is due to:
A)the acceleration of the universe
B)the presence of mass
C)the rotation of the universe
D)the curvature of spacetime
E)the speed of light

Free

Multiple Choice