Deck 13: Gravitation

Question 1

The approximate value of g at an altitude above Earth equal to one Earth diameter is:

A) 9.8 m/s²
B) 4.9 m/s²
C) 2.5 m/s²
D) 1.9 m/s²
E) 1.1 m/s²

Answer 1

1.1 m/s²

Question 2

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

Answer 2

the mass of the Sun

Question 3

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

Answer 3

in the absence of air resistance all bodies at a given location fall with the same acceleration

Question 4

Suitable units for the gravitational constant G are:

A) kg.m/s²
B) m/s²
C) N.s/m
D) kg.m/s
E) m³/(kg.s²)

Question 5

Let F₁ be the magnitude of the gravitational force exerted on the Sun by Earth and F₂ be the magnitude of the force exerted on Earth by the Sun. Then:

A) F₁ is much greater than F₂
B) F₁ is slightly greater than F₂
C) F₁ is equal to F₂
D) F₁ is slightly less than F₂
E) F₁ is much less than F₂

Question 6

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

A) R²/M
B) M/R²
C) MR²
D) M/R
E) R/M

Question 7

The gravitational constant G has the derived units

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

Question 8

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

Question 9

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

Question 10

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

Question 11

In the formula F = Gm₁m₂/r², 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 Earth

Question 12

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

Question 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

Question 14

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

Question 15

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

Question 16

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

Question 17

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) $\uparrow$
B) $\downarrow$
C) $\leftarrow$
D) $\rightarrow$
E) none of these directions

Question 18

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/s²
B) 1.4 m/s²
C) 2.0 m/s²
D) 3.7 m/s²
E) 26 m/s²

Question 19

Suppose you have a pendulum clock which keeps correct time on Earth (acceleration due to gravity = 9.8 m/s²). Without changing the clock, you take it to the Moon (acceleration due to gravity = 1.6 m/s²). For every hour interval (on Earth) the Moon clock will record:

A) (9.8/1.6) h
B) 1 h
C)
D) (1.6/9.8) h
E)

Question 20

A mass m is located at the origin; a second mass m is at x = d. A third mass m is above the first two so the three masses form an equilateral triangle. What is the net gravitational force on the third mass?

A) 2Gm²/d²
B) Gm²/d²
C) Gm²/d²
D) Gm²/2d²
E) Gm²/2d²

Question 21

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

Question 22

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

Question 23

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 r²
C) proportional to r
D) proportional to 1/r
E) proportional to 1/r²

Question 24

Neglecting air resistance, the escape speed from a certain planet for an empty space vehicle is 1.12 *10⁴ 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 * 10³ m/s
B) 1.12 * 10⁴ m/s
C) 3.36 * 10⁴ m/s
D) 1.01 *10⁵ m/s
E) 1.40*10¹² m/s

Question 25

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

Question 26

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

Question 27

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.

Question 28

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

Question 29

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

Question 30

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) 4Gm²/d
B) -4Gm²/d
C) 8Gm²/d
D) -8Gm²/d
E) zero

Question 31

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

Question 32

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

Question 33

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

Question 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

Question 35

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

Question 36

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

Question 37

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

Question 38

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_Em/R
C) GM_Em/2R
D) −GM_Em/R
E) −GM_Em/2R

Question 39

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

Question 40

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

Question 41

Two planets are orbiting a star in a distant galaxy. The first has a semimajor axis of 150 * 10⁶ km, an eccentricity of 0.20, and a period of 1.0 Earth years. The second has a semimajor axis of 250 *10⁶ 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 yr

Question 42

A planet in another solar system orbits a star with a mass of 4.0 * 10³⁰ kg. At one point in its orbit it is 250* 10⁶ km from the star and is moving at 35 km/s. Take the universal gravitational constant to be 6.67 * 10^-11 m²/s² .0 kg and calculate the semimajor axis of the planet's orbit. The result is:

A) 79 * 10⁶ km
B) 140 * 10⁶ km
C) 290 * 10⁶ km
D) 320 * 10⁶ km
E) 590 * 10⁶ km

Question 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

Question 44

The orbit of a certain a satellite has a semimajor axis of 1.5 *10⁷ m and an eccentricity of 0.20. Its perigee (minimum distance) and apogee (maximum distance) are respectively:

A) 1.2 *10⁷ m, 1.8 *10⁷ m
B) 3.0 *10⁶ m, 1.2 *10⁷ m
C) 6.0* 10⁶ m, 9.0 *10⁶ m
D) 1.0 *10⁷ m, 1.2 *10⁷ m
E) 9.6 * 10⁶ m, 1.8 * 10⁷ m

Question 45

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

Question 46

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

Question 47

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) L₂ > L₁ and K₂ > K₁
B) L₂ > L₁ and K₂ = K₁
C) L₂ = L₁ and K₂ = K₁
D) L₂ < L₁ and K₂ = K₁
E) L₂ = L₁ and K₂ > K₁

Question 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

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

Question 54

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

Question 55

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