Question 1

An astronaut in an orbiting space-craft feels "weightless" because she:

Accepted Answer

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 
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 D

Question 2

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:

Accepted Answer

A)  3.5 km/s 
B)  5.5 km/s 
C)  7.1 km/s 
D)  10 km/s 
E)  11 km/s 
A)  3.5 km/s 
B)  5.5 km/s 
C)  7.1 km/s 
D)  10 km/s 
E)  11 km/s E

Question 3

Each of the four corners of a square with edge a is occupied by a point mass m. There is a fifth mass, also m, at the center of the square. To remove the mass from the center to a point far away the work that must be done be an external agent is given by:

Accepted Answer

A)  4Gm2/a 
B)  -4Gm2/a 
C)    
D)    
E)  4Gm2/a2 
A)  4Gm2/a 
B)  -4Gm2/a 
C)    
D)    
E)  4Gm2/a2 C

Question 4

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

Accepted Answer

A)  R2/M 
B)  M/R2 
C)  MR2 
D)  M/R 
E)  R/M 
A)  R2/M 
B)  M/R2 
C)  MR2 
D)  M/R 
E)  R/M

Question 5

Of the following where would the weight of an object be the least?

Accepted Answer

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 
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 6

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 the work done by an external agent does work given by:

Accepted Answer

A)  4Gm2/d 
B)  -4Gm2/d 
C)  8Gm2/d2 
D)  -8Gm2/d2 
E)  zero 
A)  4Gm2/d 
B)  -4Gm2/d 
C)  8Gm2/d2 
D)  -8Gm2/d2 
E)  zero

Question 7

In the formula F = Gm1m2/r2, the quantity G:

Accepted Answer

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 
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 8

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?

Accepted Answer

A)  3.73 * 103 m/s 
B)  1.12 *104 m/s 
C)  3.36 *104 m/s 
D)  9.98 * 104 m/s 
E)  1.40 * 1012 m/s 
A)  3.73 * 103 m/s 
B)  1.12 *104 m/s 
C)  3.36 *104 m/s 
D)  9.98 * 104 m/s 
E)  1.40 * 1012 m/s

Question 9

A planet travels in an elliptical orbit about a star X as shown. The magnitude of the acceleration of the planet is:

Accepted Answer

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 
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 10

Consider the statement: "Earth moves in a stable orbit around the Sun and is therefore in equilibrium". The statement is:

Accepted Answer

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 
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 11

For a planet in orbit around a star the perihelion distance is rp and its speed at perihelion is vp. The aphelion distance is ra and its speed at aphelion is va. Which of following is true?

Accepted Answer

A)  va = vp 
B)  va/ ra = vp/rp 
C)  va ra = vp rp 
D)  va/ r2a = vp/r2p 
E)  va r2a = vp/r2p 
A)  va = vp 
B)  va/ ra = vp/rp 
C)  va ra = vp rp 
D)  va/ r2a = vp/r2p 
E)  va r2a = vp/r2p

Question 12

If Earth were to rotate only 100 times per year about its axis:

Accepted Answer

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 
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 artificial satellite of Earth nears the end of its life due to air resistance. While still in orbit:

Accepted Answer

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 
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

Question 14

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:

Accepted Answer

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 
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 15

A spherical shell has inner radius R1, outer radius R2, and mass M, distributed uniformly throughout the shell. The magnitude of the gravitational force exerted on the shell by a point particle of mass m, located a distance d from the center, outside the inner radius and inside the outer radius, is:

Accepted Answer

A)  0 
B)  GMm/d2 
C)    
D)    
E)    
A)  0 
B)  GMm/d2 
C)    
D)    
E)

Question 16

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:

Accepted Answer

A)  not dependent on r 
B)  proportional to r2 
C)  proportional to r 
D)  proportional to 1/r 
E)  proportional to 1/r2 
A)  not dependent on r 
B)  proportional to r2 
C)  proportional to r 
D)  proportional to 1/r 
E)  proportional to 1/r2

Question 17

The mass of an object:

Accepted Answer

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 
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 18

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:

Accepted Answer

A)  10 N 
B)  30 N 
C)  90 N 
D)  270 N 
E)  810 N 
A)  10 N 
B)  30 N 
C)  90 N 
D)  270 N 
E)  810 N

Question 19

Suitable units for the gravitational constant G are:

Accepted Answer

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

Question 20

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:

Accepted Answer

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

Exam 13: Gravitation

An astronaut in an orbiting space-craft feels "weightless" because she:

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:

Each of the four corners of a square with edge a is occupied by a point mass m. There is a fifth mass, also m, at the center of the square. To remove the mass from the center to a point far away the work that must be done be an external agent is given by:

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

Of the following where would the weight of an object be the least?

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 the work done by an external agent does work given by:

In the formula F = Gm1m2/r2, the quantity G:

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 planet travels in an elliptical orbit about a star X as shown. The magnitude of the acceleration of the planet is:

Consider the statement: "Earth moves in a stable orbit around the Sun and is therefore in equilibrium". The statement is:

For a planet in orbit around a star the perihelion distance is rp and its speed at perihelion is vp. The aphelion distance is ra and its speed at aphelion is va. Which of following is true?

If Earth were to rotate only 100 times per year about its axis:

An artificial satellite of Earth nears the end of its life due to air resistance. While still in orbit:

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:

The mass of an object:

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:

Suitable units for the gravitational constant G are:

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:

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In the formula F = Gm₁m₂/r², the quantity G:

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?

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?

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: