AL-MC-Solid / p.1
1.
(88-I-10)
B.
The force between molecules is
repulsive when r <
C.
The average separation between the
molecules is
D.
r0 .
r0 .
The energy required to separate two
molecules completely is E.
Three wires of different material, but of the same
E.
length and cross-sectional area are stretched until
The larger the value of E, the higher is
the melting point of the substance.
they break. Their stress/strain curves are shown in
the figure above. If
E1 , E2 and E3 represent
3.
(90-I-8)
Two wires X and Y of the same length and of
the energy required to break wire 1, wire 2 and
the same elastic metal are each stretched to the
wire 3 respectively, which of the following is
same tension. The diameter of wire X is half
correct?
that of wire Y. The ratio of the elastic potential
energy stored in wire X to that stored in wire
A.
E1 > E2 > E3
B.
E3 > E2 > E1
C.
E2 > E1 > E3
D.
E2 > E3 > E1
E.
E3 > E1 > E2
Y is
4.
A.
1:1
B.
1:2
C.
1:4
D.
2:1
E.
4:1
(91-I-11)
The breaking stress of a steel wire is
5.0  108 Nm 2 . If the steel wire is replaced by a
similar piece which is twice as long, which of the
2.
(88-I-11)
following statements is/are correct?
(1)
The extension when the longer wire breaks is
the same as for the shorter wire.
(2)
The work done in stretching the longer wire
to the breaking point is the same as for the
shorted wire.
(3)
The graph above shows how the potential energy
The stress needed to break the longer wire is
5.0  108 Nm 2 .
between molecules of a substance varies with their
separation. Which of the following is an
A. (1), (2) and (3)
INCORRECT inference from the graph?
B. (1) and (2) only
C. (2) and (3) only
A.
No resultant force acts on each
molecule when r =
r0 .
D. (1) only
E. (3) only
AL-MC-Solid / p.2
5.
(91-I-12)
ions must be pushing them apart.
(2)
At C the potential energy curve is a
minimum, so a supply of energy is needed
either to increase or decrease the distance
between ions.
(3)
At B, the potential energy is zero, so here
any repulsive force between the ions must be
A suspended fibre was stretched by an increasing
zero.
load attached to the bottom end. Then it was
allowed to contract by slowly reducing the load. A
A.
(1), (2) and (3)
stress-strain graph was obtained as shown. Which
B.
(1) and (2) only
one of the following conclusions may be deduced
C.
(2) and (3) only
from the graph?
D.
(1) only
E.
(3) only
(1)
All the work done in stretching the fibre is
converted into potential energy.
(2)
7.
(91-I-15)
More work is done in stretching than is
recovered in contracting.
(3)
The temperature of the fibre rises after it has
been stretched and allowed to contract for a
few times.
A.
(1), (2) and (3)
B.
(1) and (2) only
C.
(2) and (3) only
D.
(1) only
In an idealised atomic model of the material of a
E.
(3) only
wire, each atom is in equilibrium at a distance x
from its nearest neighbors, both in its own layer
6.
(91-I-14)
and in the layer above or below. There are n atoms
The graph shows how the potential energy of a pair
per unit area within each layer. If the force required
of ions varies with the distance between them.
to increase the separation between two atoms from
x to ( x  x ) is ( kx ) , what is the
longitudinal stress in the wire?
A.
B.
Which of the following arguments about the points
A, B and C marked on the graph is/are correct?
(1)
From A to B the potential energy falls with
distance, so here the net force between the
C.
D.
E.
x
x
kx
nkx
x2
nkx
k
x
AL-MC-Solid / p.3
8.
(92-I-12)
11.
A ductile fracture occurs
(95-IIA-22)
A uniform wire is clamped at both ends which are
0.4 m apart. The tension in the wire is 65 N and the
9.
slow crack propagation.
(2)
when dislocations are not free to move.
vibrations, the frequency of the fundamental note
(3)
after a brittle fracture occurs.
obtained is 160 Hz. The density of the wire is
after appreciable plastic deformation, by
A.
(1), (2) and (3)
A.
5600 kgm-3
B.
(1) and (2) only
B.
8800 kgm-3
C.
(2) and (3) only
C.
12600 kgm-3
D.
(1) only
D.
14000 kgm-3
E.
(3) only
E.
22000 kgm-3
(93-I-43)
Which of the following materials satisfies the
description : ductile, strong and stiff?
10.
7
area of its cross-section is 4.5  10 m . When
the wire is plucked to produce transverse
(1)
A.
steel
B.
diamond
C.
glass
D.
concrete
E.
wood
(94-IIA-22)
A uniform wire of force constant k and Young
modulus E is cut into two shorter wires of equal
length. If they are arranged side by side and treated
as a single wire combination, what are the force
constant and the Young modulus for this
combination?
Force constant Young modulus
A.
k
E
B.
2k
E
C.
2k
2E
D.
4k
E
E.
4k
2E
2
AL-MC-Solid / p.4
12.
(95-IIA-24)
13.
(95-IIA-33)
In which of the following graphs does the area of
A uniform wire is stretched under tension. The
the shaded part represent energy?
strain in the wire depends on


(1)
the Young modulus of the wire.
(2)
The cross-sectional area of the wire
(3)
The unstretched length of the wire.
A.
(1) only
B.
(3) only
= strain in a wire
C.
(1) and (2) only
= stress applied to the wire
D.
(2) and (3) only
E.
(1), (2) and (3)
14.
I = current passing through a coil
 = magnetic flux through the coil
(96-IIA-36)
The potential energy, U, of a pair of atoms as a
function of their separation, r, is shown for two
crystalline solids P and Q. From these curves alone,
one may conclude that
(1)
the equilibrium separation of the atoms in P
is greater than that in Q.
(2)
P is stiffer than Q.
(3)
the energy required to separate two atoms of
P in equilibrium is more than that for Q.
Q = charge on a capacitor
V = p.d. between the plates
A.
(1) only
B.
(3) only
A.
(1) only
C.
(1) and (2) only
B.
(3) only
D.
(2) and (3) only
C.
(1) and (2) only
E.
(1), (2) and (3)
D.
(2) and (3) only
E.
(1) and (3) only
AL-MC-Solid / p.5
15.
(96-IIA-38)
hanging a weight from its lower end. Which of the
Of the three common materials, copper, glass and
following would put a greater strain on the wire?
rubber, which two best illustrate the properties
(The Young modulus of steel is greater than that of
described in the following statements when each is
brass.)
stretched under room temperature?
(1)
(1)
It obeys Hooke’s law almost up to its
length.
breaking point.
(2)
Using a steel wire of greater unstretched
(2)
It tolerates a large strain when exhibiting
Using a steel wire of greater cross-sectional
area.
elastic behaviour.
(3)
Replacing the steel wire with a brass wire of
the same unstretched length and
16.
(1)
(2)
cross-sectional area.
A.
copper
glass
B.
copper
rubber
A.
(1) only
C.
glass
copper
B.
(3) only
D.
glass
rubber
C.
(1) and (2) only
E.
rubber
glass
D.
(2) and (3) only
E.
(1), (2) and (3)
(97-IIA-20)
The diagram below shows the stress-strain graphs up
18.
(98-IIA-37)
to the breaking point for two cylindrical rods made
from materials P and Q respectively, which have the
same diameter and original length.
The figure shows the force-separation graph for a
Which of the two materials
pair of atoms in a material. Which of the following
features is most closely related to the stiffness and
17.
(1)
is the more ductile
(2)
exhibits greater stiffness
(3)
has the greater strength?
the tensile strength of the material?
(1)
the value of the separation at P
(2)
the value of the separation at Q
(1)
(2)
(3)
(3)
the value of the slope of the graph at P
A.
Q
P
Q
(4)
the value of the force at Q
B.
P
Q
P
C.
Q
P
P
D.
P
P
Q
A.
(1)
(2)
E.
Q
Q
P
B.
(1)
(4)
C.
(3)
(2)
(98-IIA-36)
D.
(3)
(4)
A uniform vertical steel wire is stretched by
E.
(4)
(3)
Stiffness
Tensile strength
AL-MC-Solid / p.6
19.
(00-IIA-36)
Given that a and b are positive constants, and
The average stress in the legs of a man standing
repulsive force is taken as positive, which of the
upright is S. If the dimensions of the man are
following correctly expresses in mathematical
doubled while the average density of the body
form the interatomic potential energy of a pair of
remains the same, the average stress in the legs
atoms?
would be
A.
S/2
B.
S
C.
2S
D.
4S
E.
A.
a
b
 4
7
r
r
B.

r
C.
8S
a
r
D.
20.
a

6
a

(00-IIA-37)
r
Let r be the separation of two molecules in a solid
E.
and U be the intermolecular potential energy of
a
r
6
5
5

b

r3
b
r3

b
r2
b
r2
these two molecules. When r = ro , the attractive
force between the two molecules is equal to their
repulsive force. Let U = 0 when r = ro . Which of
the following statements is INCORRECT?
22.
(01-IIA-36)
In an experiment to determine the Young modulus
for a steel wire, a student obtained the following
A.
U is non-negative for all values of r.
B.
When r < ro , U increases as r
C.
D.
E.
data:
=
1.96  0.01m
decreases.
length of steel wire
When r > ro , U increases as r
diameter of steel wire =
0.61  0.01mm
increases.
mass of the load
=
10.00  0.01kg
When r is very large, U is close to
extension
=
3.9  0.1mm
zero.
acceleration of free fall =
9.8  0.1 ms 2
When U is very large, the force
between the two molecules is
Which of the following leads to the greatest
repulsive.
uncertainty in the calculated value of the Young
modulus?
21.
(01-IIA-35)
The interatomic force between pairs of similar
A. measurement of length
atoms consists of two components. These are
B. measurement of diameter
C. measurement of load
(1)
a short-range repulsive force which varies
inversely as r
(2)
6
a long-range attractive force which varies
inversely as r 3 , where r = interatomic
separation.
D. measurement of extension
E. assumed value of the acceleration of free fall
AL-MC-Solid / p.7
23.
equilibrium spacing?
(01-IIA-37)
A.
B.
C.
D.
25.
.
The graph above shows the tensile stress-tensile
strain curves for three materials X, Y and Z up to
their breaking points. Which of the following
statements is/are correct?
24.
(1)
X is stiffer than Y.
(2)
Y is stronger than Z.
(3)
Z can be stretched to twice its
(03-IIA-40)
Copper plates can be made by hammering
solid copper but glass fibres can only be made
by drawing from molten glass. Which
comparison below is the best explanation for
this difference?
A.
original length without breaking.
B.
A.
(1) only
C.
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
E.
(1), (2) and (3)
(03-IIA-39)
The graph shows how the mutual interatomic
force F between two atoms varies with their
separation r. F is taken to be positive when it
is repulsive. A1, A2 and A3 represent the areas
of the respective regions as shown.
Which of the following represents the energy
required to separate the atoms to infinity,
assuming that they are originally at their
A2 + A3
A1 + A2 – A3
A1 + A2 + A3
A2 + A3 – A1
D.
Copper has a definite melting point
while glass does not.
Solid copper has a smaller young
modulus than solid glass.
Solid copper shows plastic deformation
while solid glass does not.
Solid copper extends elastically more
than solid glass under the same stress.