1) What are the SI units of the shear modulus?
a) N/m2
b) N/m
c) N ⋅ m
d) N/m3
e) N ⋅ m2
2) Complete the following statement: Young's modulus cannot be applied to
a) a stretched wire.
b) a compressed rod.
c) a bending beam.
d) a compressed liquid.
e) a stretched rubber band.
3) A cable stretches by an amount d when it supports a crate of mass M. The cable is then cut in
half. If the same crate is supported by either half of the cable, by how much will the cable
stretch?
a) d
b) d/2
c) d/4
d) 2d
e) 4d
4) A cable stretches by an amount d as it supports a crate of mass M. The cable is cut in half.
What is the mass of the load that can be supported by either half of the cable if the cable
stretches by an amount d?
a) M/4
b) M/2
c) M
d) 2M
e) 4M
5) A cable stretches by an amount d when it supports a crate of mass M. The cable is replaced
by another cable of the same material having the same length and twice the diameter. If the
same crate is supported by the thicker cable, by how much will the cable stretch?
a) d/4
b) d/2
c) d
d) 2d
e) 4d
6) A cable stretches by an amount d when it supports a crate of mass M. The cable is replaced
by another cable of the same material having the same length and twice the diameter. What is
the mass of the load that can be supported by the thicker cable if it stretches by an amount d?
a) M/4
b) M/2
c) M
d) 2M
e) 4M
7) The maximum compressional stress that a bone can withstand is 1.6 × 108 N/m2 before it
breaks. A thighbone (femur), which is the largest and longest bone in the human body, has a
cross sectional area of 7.7 × 10-4 m2. What is the maximum compressional force that can be
applied to the thighbone?
a) 2.1 × 1011 N
b) 1.2 × 105 N
c) 4.8 × 1012 N
d) 3.0 × 103 N
e) This cannot be determined since Young’s modulus is not given.
8) Young's modulus of nylon is 5 × 109 N/m2. A force of 5 × 105 N is applied to a 2-m length of
nylon of cross sectional area 0.1 m2. By what amount does the nylon stretch?
a) 2 × 10-1 m
b) 2 × 10-2 m
c) 2 × 10-3 m
d) 2 × 10-4 m
e) 2 × 10-5 m
9) The radius of a sphere of lead (B = 4.2 × 1010 N/m2) is 1.000 m on the surface of the earth
where the pressure is 1.01 × 105 N/m2. The sphere is taken by submarine to the deepest part
of the ocean to a depth of 1.10 × 104 m where it is exposed to a pressure is 1.25 × 108 N/m2.
What is the volume of the sphere at the bottom of the ocean?
a) 4.176 m3
b) 4.189 m3
c) 1.25 × 10-2 m3
d) 0.134 m3
e) 0.988 m3
10) The shear modulus of aluminum is 2.4 × 1010 N/m2. An aluminum nail of radius 7.5 × 10-4 m
projects 0.035 m horizontally outward from a wall. A man hangs a wet raincoat of weight
25.5 N from the end of the nail. Assuming the wall holds its end of the nail, what is the
vertical deflection of the other end of the nail?
a) 1.8 × 10-3 m
b) 3.3 × 10-2 m
c) 7.9 × 10-6 m
d) 4.2 × 10-4 m
e) 2.1 × 10-5 m
Questions 11 through 13 pertain to the situation described below:
A 5.0 × 102-N object is hung from the end of a wire of cross-sectional area 0.010 cm2. The wire
stretches from its original length of 200.00 cm to 200.50 cm.
11) What is the stress on the wire?
a) 5.0 × 102 N/m2
b) 1.0 × 106 N/m2
c) 1.0 × 108 N/m2
d) 5.0 × 106 N/m2
e) 5.0 × 108 N/m2
12) What is the elongation strain on the wire?
a) 1.0 × 102
b) 1.0 × 10-2
c) 5.0 × 102
d) 2.5 × 10-3
e) 4.0 × 102
13) Determine the Young's modulus of the wire.
a) 1.0 × 1011 N/m2
b) 1.0 × 109 N/m2
c) 2.0 × 1011 N/m2
d) 2.0 × 109 N/m2
e) 5.0 × 1012 N/m2
Questions 14 and 15 pertain to the situation described below:
A plastic box has an initial volume of 2.00 m3. It is then submerged below the surface of a liquid
and its volume decreases to 1.96 m3.
14) What is the volume strain on the box?
a) 0.02
b) 0.04
c) 0.2
d) 0.4
e) 0.98
15) Complete the following statement: In order to calculate the "stress" on the box, in addition to
the information given, one must also know
a) the mass of the box.
b) the bulk modulus of the material from which the box is made.
c) the shear modulus of the material from which the box is made.
d) the Young's modulus of the material from which the box is made.
e) the bulk modulus of the liquid.
16) Complete the following statement: In general, the term stress refers to
a) a change in volume.
b) a change in length.
c) a force per unit area.
d) a fractional change in length.
e) a force per unit length.
17) Which one of the following statements concerning Hooke's law is false?
a) Hooke’s law relates stress and strain.
b) Hooke’s law is valid only for springs.
c) Hooke’s law can be verified experimentally.
d) Hooke’s law can be applied to a wide range of materials.
e) Hooke’s law is valid only within the elastic limit of a given
material.
18) A cylinder with a radius of 0.120 m is placed between the plates of a
hydraulic press as illustrated in the drawing. A 4.45 × 105-N force is
applied to the cylinder. What is the pressure on the end of the cylinder
due to the applied force?
a) 9.84 × 106 Pa
b) 3.13 × 105 Pa
c) 6.18 × 106 Pa
d) 5.34 × 104 Pa
e) 3.71 × 106 Pa
19) Stress can be measured in:
a) N/m2
b) N·m2
c) N/m
d) N·m
e) none of these (it is unitless)
20) Strain can be measured in:
a) N/m2
b) N·m2
c) N/m
d) N·m
e) none of these (it is unitless)
21) Young’s modulus can be correctly given in:
a) N·m
b) N/m2
c) N·m/s
d) N/m
e) Joules
22) Young’s modulus is a proportionality constant that relates the force per unit area applied
perpendicularly at the surface of an object to:
a) the shear
b) the fractional change in volume
c) the fractional change in length
d) the pressure
e) the spring constant
23) Young’s modulus can be used to calculate the strain for a stress that is:
a) just below the ultimate strength
b) just above the ultimate strength
c) well below the yield strength
d) well above the yield strength
e) none of the above
24) The ultimate strength of a sample is the stress at which the sample:
a) returns to its original shape when the stress is removed
b) remains underwater
c) breaks
d) bends 180◦
e) does none of these
25) A certain wire stretches 0.90 cm when outward forces with magnitude F are applied to each
end. The same forces are applied to a wire of the same material but with three times the
diameter and three times the length. The second wire stretches:
a) 0.10 cm
b) 0.30 cm
c) 0.90 cm
d) 2.7 cm
e) 8.1 cm
26) A force of 5000N is applied outwardly to each end of a 5.0-m long rod with a radius of 34.0
mm and a Young’s modulus of 125 × 108 N/m2. The elongation of the rod is:
a) 0.0020 mm
b) 0.0040 mm
c) 0.14 mm
d) 0.55 mm
e) 1.42 mm
27) A 4.0-m long steel beam with a cross-sectional area of 1.0 × 10-2 m2 and a Young’s modulus
of 2.0 × 1011 N/m2 is wedged horizontally between two vertical walls. In order to wedge the
beam, it is compressed by 0.020 mm. If the coefficient of static friction between the beam
and the walls is 0.70 the maximum mass (including its own) it can bear without slipping is:
a) 0
b) 3.6kg
c) 36 kg
d) 71 kg
e) 710 kg
28) Two supports, made of the same material and initially of equal length, are 2.0m apart. A stiff
board with a length of 4.0m and a mass of 10 kg is placed on the supports, with one support
at the left end and the other at the midpoint. A block is placed on the board a distance of
0.50m from the left end. As a result, the board is horizontal. The mass of the block is:
a) zero
b) 2.3kg
c) 6.6kg
d) 10 kg
e) 20 kg
29) The bulk modulus is a proportionality constant that relates the pressure acting on an object
to:
a) the shear
b) the fractional change in volume
c) the fractional change in length
d) Young’s modulus
e) the spring constant
30) A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5×109
N/m2. When it is subjected to a pressure of 3.0 × 105 Pa its volume is:
a) 7.31 cm3
b) 7.99931 cm3
c) 8.00069 cm3
d) 8.69 cm3
e) none of these
31) A cube with 2.0-cm sides is made of material with a bulk modulus of 4.7 × 105 N/m2. When
it is subjected to a pressure of 2.0 × 105 Pa the length of its any of its sides is:
a) 0.85 cm
b) 1.15 cm
c) 1.66 cm
d) 2.0 cm
e) none of these
32) To shear a cube-shaped object, forces of equal magnitude and opposite directions might be
applied:
a) to opposite faces, perpendicular to the faces
b) to opposite faces, parallel to the faces
c) to adjacent faces, perpendicular to the faces
d) to adjacent faces, neither parallel or perpendicular to the faces
e) to a single face, in any direction
33) A shearing force of 50N is applied to an aluminum rod with a length of 10 m, a cross-
sectional area of 1.0 × 10-5 m, and a shear modulus of 2.5 × 1010 N/m2. As a result the rod is
sheared through a distance of:
a) zero
b) 1.9mm
c) 1.9 cm
d) 19 cm
e) 1.9m
34) A 0.750-kg object hanging from a vertical spring is observed to oscillate with a period of
2.00 s. When the 0.750-kg object is removed and replaced by a 1.25-kg object, what will be
the period of oscillation?
a) 1.55 s
b) 2.58 s
c) 3.32 s
d) 4.38 s
e) 7.45 s
35) Two point masses m and M are separated by a distance d. If the distance between the masses
is increased to 3d, how does the gravitational force between them change?
(a) The force will be one-third as great.
(b) Theforcewillbeone-ninthasgreat.
(c) The force will be three times as great.
(d) Theforcewillbeninetimesasgreat.
(e) It is impossible to determine without knowing the numerical values of m, M, and d.
36) Two point masses m and M are separated by a distance d. If the separation d remains fixed
and the masses are. increased to the values 3m and 3M respectively, how does the
gravitational force between them change?
(a) The force will be one-third as great.
(b) The force will be one-ninth as great.
(c) The force will be three times as great.
(d) The force will be nine times as great.
(e) It is impossible to determine without knowing the numerical values of m, M, and d.
37) An astronaut orbits the earth in a space capsule whose height above the earth is equal to the
earth's radius. How does the mass of the astronaut in the capsule compare to her mass on the
earth?
(a) Her mass is equal to her mass on earth.
(b) Her mass is equal to one-fourth her mass on earth.
(c) Her mass is equal to one-half of her mass on earth.
(d) Her mass is equal to one-third of her mass on earth.
(e) Her mass is equal to one-sixteenth her mass on earth.
38) What is the magnitude of the gravitational force acting on a 79.5-kg student due to a 60.0-kg
student sitting 2.25 m away in the lecture hall?
(a) 3.14×10−9 N
(b) 7.91×10−10 N
(c) 6.29×10−8 N
(d) 2.82×10−8 N
(e) 1.41×10−7 N
39) Which of the following best describes Kepler's first law?
a) Planets move in perfect circles around the Sun.
b) Planets move in elliptical orbits with the Sun at the center.
c) Planets move in elliptical orbits with the Sun at one of the foci.
d) Planets move in parabolic paths around the Sun.
40) According to Kepler's third law, how does the square of the orbital period of a planet relate to
the cube of the semi-major axis of its orbit?
a) T^3 ∝ a^2
b) T^2 ∝ a^3
c) T^2 ∝ a^2
d) T^3 ∝ a
41) What is the relationship between the gravitational force (F), the masses of two objects (m1
and m2), and the distance between their centers (r)?
a) F ∝ m1 × m2
b) F ∝ m1 / r^2
c) F ∝ m2 / r
d) F ∝ 1 / (m1 × m2 × r)
42) How does Kepler's first law relate to the gravitational force between a planet and the Sun?
a) It explains the elliptical shape of planetary orbits due to gravitational attraction.
b) It explains the variation in orbital speed of planets.
c) It defines the relationship between the orbital period and the distance from the Sun.
d) It determines the orientation of the planets in the solar system.
43) How does Kepler's third law relate to the gravitational force between a planet and the Sun?
a) It shows that the gravitational force increases with the square of the distance.
b) It demonstrates a direct relationship between the gravitational force and the orbital period.
c) It indicates an inverse relationship between the gravitational force and the mass of the planet.
d) It illustrates the relationship between the gravitational force and the eccentricity of the orbit.
44) A pendulum is transported from sea-level, where the acceleration due to gravity g is 9.80
m/s2, to the bottom of Death Valley. At this location, the period of the pendulum is
decreased by 3.00%. What is the value of g in Death Valley?
a) 9.22 m/s2
b) 9.51 m/s2
c) 9.80 m/s2
d) 10.1 m/s2
e) 10.4 m/s2
45) In a certain clock, a pendulum of length L1 has a period T1 = 0.95 s. The length of the pendulum
is adjusted to a new value L2 such that T2 = 1.0 s. What is the ratio L2/L1?
a) 1.0
b) 1.3
c) 0.95
d) 1.1
e) 0.90
46) A simple pendulum consists of a ball of mass m suspended from the ceiling using a string of
length L. The ball is displaced from its equilibrium position by a small angle θ. What is the
magnitude of the restoring force that moves the ball toward its equilibrium position and
produces simple harmonic motion?
a) kx
b) mg(cos θ)
c) mgL(sin θ)
d) mg
e) mg(sin θ)
47) A simple pendulum on earth has a period of 6.0 s. What is the approximate period of this
pendulum on the moon where the acceleration due to gravity is roughly 1/6 that of earth?
a) 1s
b) 6s
c) 36 s
d) 2.4 s
e) 15 s
48) Which one of the following terms is used to describe a system in which the degree of
damping is just enough to stop the system from oscillating?
(a) critically damped (c) slightly damped (e) resonance (b) underdamped (d) overdamped
49) Complete the following sentence: Resonance occurs in harmonic motion when
a) the system is overdamped.
b) thesystemiscriticallydamped.
c) the energy in the system is a minimum.
d) thedrivingfrequencyisthesameasthenaturalfrequencyofthesystem.
e) the energy in the system is proportional to the square of the motion's amplitude.
50) A simple harmonic oscillator with a period of 2.0 s is subject to damping so that it loses one
percent of its amplitude per cycle. About how much energy does this oscillator lose per
cycle?
a) 0.5%
b) 2.0%
c) 1.0%
d) 3.0%
e) 4.0%
