Answer Key
Gravitation
-
University:
Kentucky State University -
Course:
PHY 212 | General Physics II Academic year:
2019
-
Views:
214
Pages:
19
Author:
Focalimoicy3go
Chapter 13:
GRAVITATION
1. In the formula F = Gm1 m2 /r2 , the quantity G:
A. depends on the local value of g
B. is used only when Earth is one of the two masses
C. is greatest at the surface of Earth
D. is a universal constant of nature
E. is related to the Sun in the same way that g is related to Earth
ans: D
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
ans: B
3. 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 )
ans: E
4. 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
ans: D
5. 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 on Earth by the Moon
D. the tides due to the Moon
E. the apple hitting Newton on the head.
ans: C
Chapter 13:
GRAVITATION
193 6. A particle might be placed
1. inside a uniform spherical shell of mass M , but not at the center
2. inside a uniform spherical shell of mass M , at the center
3. outside a uniform spherical shell of mass M , a distance r from the center
4. outside a uniform solid sphere of mass M , a distance 2r from the center
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
ans: D
7. Three particles, two with mass m and one with 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.
•m
d
•
M
d
•
m
d
•
m
•
m
1
A.
B.
C.
D.
E.
1, 2, 3,
2, 1, 3,
2, 1, 4,
2, 3, 4,
2, 3, 2,
ans: B
d
•
M
2
d
•
m
•
M
d
•
m
3
d •m
d
•
•
m
M
4
..
....
....
...
....
.
.
.
..
....
...
..............................................................
4
4
3
2
4
8. 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:
y
•M
•
m
A.
B.
C.
D.
E.
194
↑
↓
←
→
none of these directions
ans: B
Chapter 13:
GRAVITATION
•
m
•
m
•
m
x 9. 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
ans: C
10. Let
is:
A.
B.
C.
D.
E.
M denote the mass of Earth and let R denote its radius. The ratio g/G at Earth’s surface
R2 /M
M/R2
M R2
M/R
R/M
ans: B
11. Venus has a mass of about 0.0558 times the mass of Earth and a diameter of about 0.381 times
the diameter of Earth. The acceleration of a body falling near the surface of Venus is about:
2
A. 0.21 m/s
2
B. 1.4 m/s
2
C. 2.8 m/s
2
D. 3.8 m/s
2
E. 25 m/s
ans: D
12. The approximate value of g at an altitude above Earth equal to one Earth diameter is:
2
A. 9.8 m/s
B. 4.9 m/s2
C. 2.5 m/s2
2
D. 1.9 m/s
2
E. 1.1 m/s
ans: E
13. 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.
ans: E
Chapter 13:
GRAVITATION
195 14. 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 Earth masses, the mass of the planet is:
A. 2
B. 4
C. 8
D. 16
E. 32
ans: D
15. Suppose you have a pendulum clock that 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. 0
1h
C.
9.8/1.6 h
D. 0
(1.6/9.8) h
E.
1.6/9.8 h
ans: E
16. The mass of an object:
A. is slightly different at different locations on 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
ans: C
17. 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 on 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
ans: C
18. 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
ans: C
196
Chapter 13:
GRAVITATION 19. 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
ans: A
20. 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
ans: C
21. 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. At the center of Earth
D. On the Moon
E. On Jupiter
ans: C
22. Of
A.
B.
C.
D.
E.
the following where would the weight of an object be the least?
2000 miles above Earth’s surface
At the north pole
At the equator
At the center of Earth
At the south pole
ans: D
23. 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
ans: C
Chapter 13:
GRAVITATION
197 24. An
A.
B.
C.
D.
E.
astronaut in an orbiting spacecraft feels “weightless” because she:
is beyond the range of gravity
is pulled outward by centrifugal force
has no acceleration
has the same acceleration as the spacecraft
is outside Earth’s atmosphere
ans: D
25. 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 by an external agent is given by:
A. 4Gm2 /a
2
B. −4Gm
/a
√
C. 4 √
2Gm2 /a
D. −4 2Gm2 /a
E. 4Gm2 /a2
ans: C
26. 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 is given by:
A. 4Gm2 /d
B. −4Gm2 /d
C. 8Gm2 /d2
D. −8Gm2 /d2
E. zero
ans: D
27. The escape speed at the surface of Earth is approximately 8 km/s. What is the mass, in units
of Earth’s mass, of a planet with twice the radius of Earth for which the escape speed is twice
that for Earth?
A. 2
B. 4
C. 8
D. 1/2
E. 1/4
ans: C
28. 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. 3.5 km/s
B. 5.5 km/s
C. 7.1 km/s
D. 10 km/s
E. 11 km/s
ans: E
198
Chapter 13:
GRAVITATION 29. 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. 9.98 × 104 m/s
E. 1.40 × 1012 m/s
ans: B
30. An object is dropped from an altitude of one Earth radius above Earth’s surface. If M is the
mass of Earth and R is its radius the speed of the object just before it hits Earth is given by:
0
A. 0GM/R
B. 0GM/2R
C. 02GM/R
D. 0GM/R2
E.
GM/2R2
ans: A
31. 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
ans: B
32. 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
ans: D
Chapter 13:
GRAVITATION
199 33. 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
mass particle of m, located a distance d from the center, inside the inner radius, is:
A. 0
B. GM m/R12
C. GM m/d2
D. GM m/(R22 − d2 )
E. GM m/(R1 − d)2
ans: A
34. 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
mass m, located a distance d from the center, outside the outer radius, is:
A. 0
B. GM m/R12
C. GM m/d2
D. GM m/(R22 − d2 )
E. GM m/(R1 − d)2
ans: C
35. 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:
A. 0
B. GM m/d2
C. GM m/(R23 − d3 )
D. GM m(d3 − R13 )/d2 (R23 − R13 )
E. GM m/(d3 − R13 )
ans: D
36. An
A.
B.
C.
D.
E.
artificial satellite of Earth releases a bomb. Neglecting air resistance, the bomb will:
strike Earth under the satellite at the instant of release
strike Earth under the satellite at the instant of impact
strike Earth ahead of the satellite at the instant of impact
strike Earth behind the satellite at the instant of impact
never strike Earth
ans: E
37. An astronaut finishes some work on the outside of his satellite, which is in circular orbit around
Earth. He leaves his wrench outside the satellite. The wrench will:
A. fall directly down to 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 Earth
ans: C
200
Chapter 13:
GRAVITATION 38. The elliptical orbit of a planet around the Sun is shown on the diagram. Which of the following
statements is true?
E
•
•D
.....................................................
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.
.
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......
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......
......
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.............................................................
A•
A.
B.
C.
D.
E.
•B
•C
the eccentricity of the orbit is less than zero
the eccentricity of the orbit is greater than 1
the sun might be at point C
the sun might be at point D
the sun might be at point B
ans: E
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 Earth does not fall into or fly away from the Sun
C. false, because Earth is rotating on its axis and no rotating body can be in equilibrium
D. false, because Earth has a considerable acceleration
E. true, because if it were not in equilibrium then buildings and structures would not be stable
ans: D
40. A planet travels in an elliptical orbit about a star X as shown. The magnitude of the acceleration
of the planet is:
Q
•
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.........
.........
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.......
......
......
......
.
.
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•
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•
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.........
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....................................................
P•
W•
•X
V
A.
B.
C.
D.
E.
•R
•
•S
•
U
•
T
greatest at point Q
greatest at point S
greatest at point U
greatest at point W
the same at all points
ans: D
Chapter 13:
GRAVITATION
201 41. 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
ans: C
42. 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
ans: A
43. 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?
Q
•
.........................................
..................
..........
........
.......
......
.....
...
.
.
....
.
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..........
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.........
.................
..........................................
P..•...........................
•R
W•
•S
V
A.
B.
C.
D.
E.
202
W and S
P and T
P and R
Q and U
V and R
ans: D
Chapter 13:
GRAVITATION
•
•
U
•
T 44. 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
ans: D
45. For a planet in orbit around a star the perihelion distance is rp ad its speed at perihelion is vp .
The aphelion distance is ra and its speed at aphelion is va . Which of the following is true?
A. va = vp
B. va /ra = vp /rp
C. va ra = vp rp
D. va /ra2 = vp /rp2
E. va ra2 = vp rp2
ans: C
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, in Earth years, is:
A. 4
B. 8
C. 16
D. 64
E. 2.52
ans: B
47. 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 years
B. 0.57 Earth years
C. 1.4 Earth years
D. 1.8 Earth years
E. 2.2 Earth years
ans: E
Chapter 13:
GRAVITATION
203 48. 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:
•
•
•
•
•
•
•
..•
.•
.•
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.•
..•
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......................
.•
.•
.•
.•
.•
..•
•
•
2•
• Earth
•1
•
•
•
•
•
•
•
•
A.
B.
C.
D.
E.
L2 > L1
L2 > L1
L2 = L 1
L2 < L1
L2 = L 1
ans: E
and
and
and
and
and
K2
K2
K2
K2
K2
> K1
= K1
= K1
= K1
> K1
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
ans: D
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 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
ans: E
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
ans: A
204
Chapter 13:
GRAVITATION 52. A spaceship is returning to Earth with its engine turned off. Consider only the gravitational
field of Earth and let M be the mass of Earth, m be the mass of the spaceship, and R be the
distance from the center of Earth. In moving from position 1 to position 2 the kinetic energy
of the spaceship increases by:
}
]
1
1
A. GM m
−
GM m/R2
R22 R12
}
]
1
1
B. GM m
+
R12 R22
R1 − R 2
C. GM m
R12
R1 − R 2
D. GM m
R1 R 2
R1 − R 2
E. GM m 2 2
R1 R2
ans: D
53. 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
ans: B
54. The orbit of a certain 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. 9.6 × 106 m, 1.0 × 107 m
D. 1.0 × 107 m, 1.2 × 107 m
E. 9.6 × 106 m, 1.8 × 107 m
ans: A
55. 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
2
constant to be 6.67 × 10−11 m2 /s · kg and calculate the semimajor axis of the planet’s orbit.
The result is:
A. 79 × 106 km
B. 160 × 106 km
C. 290 × 106 km
D. 320 × 106 km
E. 590 × 106 km
ans: C
Chapter 13:
GRAVITATION
205 Chapter 1:
MEASUREMENT
1. The SI standard of time is based on:
A. the daily rotation of the earth
B. the frequency of light emitted by Kr86
C. the yearly revolution of the earth about the sun
D. a precision pendulum clock
E. none of these
Ans: E
2. A nanosecond is:
A. 109 s
B. 10−9 s
C. 10−10 s
D. 10−10 s
E. 10−12
Ans: B
3. The SI standard of length is based on:
A. the distance from the north pole to the equator along a meridian passing through Paris
B. wavelength of light emitted by Hg198
C. wavelength of light emitted by Kr86
D. a precision meter stick in Paris
E. the speed of light
Ans: E
4. In 1866, the U. S. Congress defined the U. S. yard as exactly 3600/3937 international meter.
This was done primarily because:
A. length can be measured more accurately in meters than in yards
B. the meter is more stable than the yard
C. this definition relates the common U. S. length units to a more widely used system
D. there are more wavelengths in a yard than in a meter
E. the members of this Congress were exceptionally intelligent
Ans: C
5. Which of the following is closest to a yard in length?
A. 0.01 m
B. 0.1 m
C. 1 m
D. 100 m
E. 1000 m
Ans: C
Chapter 1:
MEASUREMENT
1 6. There is no SI base unit for area because:
A. an area has no thickness; hence no physical standard can be built
B. we live in a three (not a two) dimensional world
C. it is impossible to express square feet in terms of meters
D. area can be expressed in terms of square meters
E. area is not an important physical quantity
Ans: D
7. The SI base unit for mass is:
A. gram
B. pound
C. kilogram
D. ounce
E. kilopound
Ans: C
8. A gram is:
A. 10−6 kg
B. 10−3 kg
C. 1 kg
D. 103 kg
E. 106 kg
Ans: B
9. Which of the following weighs about a pound?
A. 0.05 kg
B. 0.5 kg
C. 5 kg
D. 50 kg
E. 500 kg
Ans: D
10. (5.0 × 104 ) × (3.0 × 106 ) =
A. 1.5 × 109
B. 1.5 × 1010
C. 1.5 × 1011
D. 1.5 × 1012
E. 1.5 × 1013
Ans: C
11. (5.0 × 104 ) × (3.0 × 10−6 ) =
A. 1.5 × 10−3
B. 1.5 × 10−1
C. 1.5 × 101
D. 1.5 × 103
E. 1.5 × 105
Ans: B
2
Chapter 1:
MEASUREMENT 12. 5.0 × 105 + 3.0 × 106 =
A. 8.0 × 105
B. 8.0 × 106
C. 5.3 × 105
D. 3.5 × 105
E. 3.5 × 106
Ans: E
13. (7.0 × 106 )/(2.0 × 10−6 ) =
A. 3.5 × 10−12
B. 3.5 × 10−6
C. 3.5
D. 3.5 × 106
E. 3.5 × 1012
Ans: E
14. The number of significant figures in 0.00150 is:
A. 2
B. 3
C. 4
D. 5
E. 6
Ans: B
15. The number of significant figures in 15.0 is:
A. 1
B. 2
C. 3
D. 4
E. 5
Ans: C
16. 3.2 × 2.7 =
A. 9
B. 8
C. 8.6
D. 8.64
E. 8.640
Ans: C
Chapter 1:
MEASUREMENT
3 17. 1.513 + 27.3 =
A. 29
B. 28.8
C. 28.9
D. 28.81
E. 28.813
( )Ans: B
18. 1 mi is equivalent to 1609 m so 55 mph is:
A. 15 m/s
B. 25 m/s
C. 66 m/s
D. 88 m/s
E. 1500 m/s
Ans: B
19. A sphere with a radius of 1.7 cm has a volume of:
A. 2.1 × 10−5 m3
B. 9.1 × 10−4 m3
C. 3.6 × 10−3 m3
D. 0.11 m3
E. 21 m3
Ans: A
20. A sphere with a radius of 1.7 cm has a surface area of:
A. 2.1 × 10−5 m2
B. 9.1 × 10−4 m2
C. 3.6 × 10−3 m2
D. 0.11 m2
E. 36 m2
Ans: C
21. A right circular cylinder with a radius of 2.3 cm and a height of 1.4 m has a volume of:
A. 0.20 m3
B. 0.14 m3
C. 9.3 × 10−3 m3
D. 2.3 × 10−3 m3
E. 7.4 × 10−4 m3
Ans: D
22. A right circular cylinder with a radius of 2.3 cm and a height of 1.4 cm has a total surface area
of:
A. 1.7 × 10−3 m2
B. 3.2 × 10−3 m2
C. 2.0 × 10−3 m3
D. 5.3 × 10−3 m2
E. 7.4 × 10−3 m2
Ans: D
4
Chapter 1:
MEASUREMENT 23. A cubic box with an edge of exactly 1 cm has a volume of:
A. 10−9 m3
B. 10−6 m3
C. 10−3 m3
D. 103 m3
E. 106 m3
Ans: B
24. A square with an edge of exactly 1 cm has an area of:
A. 10−6 m2
B. 10−4 m2
C. 102 m2
D. 104 m2
E. 106 m2
Ans: B
25. 1 m is equivalent to 3.281 ft. A cube with an edge of 1.5 ft has a volume of:
A. 1.2 × 102 m3
B. 9.6 × 10−2 m3
C. 10.5 m3
D. 9.5 × 10−2 m3
E. 0.21 m3
Ans: B
26. During a short interval of time the speed v in m/s of an automobile is given by v = at2 + bt3 ,
where the time t is in seconds. The units of a and b are respectively:
A. m · s2 ; m · s4
B. s3 /m; s4 /m
C. m/s2 ; m/s3
3
4
D. m/s ; m/s
4
5
E. m/s ; m/s
Ans: D
27. Suppose A = BC, where A has the dimension L/M and C has the dimension L/T. Then B
has the dimension:
A. T/M
B. L2 /TM
C. TM/L2
D. L2 T/M
E. M/L2 T
Ans: A
Chapter 1:
MEASUREMENT
5 28. Suppose A = B n C m , where A has dimensions LT, B has dimensions L 2 T−1 , and C has
dimensions LT2 . Then the exponents n and m have the values:
A. 2/3; 1/3
B. 2; 3
C. 4/5; −1/5
D. 1/5; 3/5
E. 1/2; 1/2
Ans: D
6
Chapter 1:
MEASUREMENT
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