KIGALI INSTITUTE OF SCIENCE AND TECHNOLOGY
INSTITUT DES SCIENCES ET TECHNOLOGIE
Avenue de l'Armée, B.P. 3900 Kigali, Rwanda
INSTITUTE EXAMINATIONS – ACADEMIC YEAR 2012-2013
MAIN EXAMINATION
FACULTY OF SCIENCE
SCIENCE 2-PHYSICS
B.Sc. in Applied Physics and applied Mathematics
YEAR I SEMESTER II
PHY3122Properties of matter
DATE: TIME: 2 HOURS
MAXIMUM MARKS = 60
INSTRUCTIONS
1.
This paper contains FOUR(4) questions.
2.
Section A is compulsory; answer any TWO(2) questions in section B.
3.
Question I counts for 30 marks, others count 15 marks each.
4.
No written materials allowed.
5.
Write all answers in the booklet provided.
6.
Do not forget to write your Registration Number.
7.
Do not write any answers on this question paper.
8.
Start a new question on a new page of booklet.
Density of water=10 3 kgm -3
Gravity acceleration g=9.8 ms -2
Page 1 of 4

SECTION A: THIS SECTION IS COMPULSORY
QUESTION I /30 marks
1.
a) Explain the next terms: stress, tensile strain, bending moment, deflection, and flexural rigidity. b) The following graph shows how the extension of a steel wire of length
1.2m and area of cross-section 0.012 mm 2 alters as a stretching force is applied. Use this graph tocalculate the modulus of elasticity c) Find an expression for the elastic (potential) energy stored (or work done) in a cylinder whose one end is fixed and the other end is twisted through an angle φ. d) A steel bar 200 mm long and 20x20 mm 2 cross section is subjected to a tensile force of 40000N in the direction of its length. Calculate its change in volume. The Poisson’s ratio of the material of the bar is ν =0.3 and modulus of elasticity Y = 2.05 x10
5
MPa. e) The cantilever beam shown below is subjected to a constant couple moment
M
0 at its free end. Determine the equation of the slope and that of the elastic curve. What are the maximum values of slope and deflection (values of slope and deflection at free end where x=L)? The boundary conditions are: at x=o, the slope and the deflection are both zero.
Page 2 of 4

Y
X f.
A solid aluminum ingot weighs 89 N in air. i.
If the density of aluminum is 2.7 × 10 3 kg/m 3
what is the volume of the ingot? ii.
The ingot is suspended from a rope and totally immersed in water.
What is the weight of the ingot in water?
(5 marks)
SECTION B: ATTEMPT ANY TWO (2) QUESTIONS
QUESTION II /15 marks
1.
Let us consider a small portion of the beam bounded by two transverse sections AB and CD close to each other. After bending, ABis elongated to
A′B′ and CD is shortened to C′D′.Let the small portion, under consideration; be bent in the form of a circular arc, subtending an angle dθ at the center of curvature O. Let R be the radius of curvature of the neutral surface E′F′. i.
Considering a filament GH between E’F’ and C’G’, show that longitudinal normal strain ε varies linearly with the distance y from the neutral surface; ii.
Show that the normal stress in any fiber is proportional to the distance of the fiber y from the neutral axis;
Page 3 of 4

iii.
By considering an elemental area ‘da’ at the distance ‘y’ from the neutral axis, derive the Bernoulli-Euler bending equation.
(10 marks)
2.
Two clamps are fastened near the ends of a rectangular steel rod 10cm long.
Therectangular cross sectional area of the rod is 5cm 2 . A force of 80N is applied on each of these clamps parallel to this area but in opposite direction. Determine i.
Shear stress ii.
Shear strain and iii.
the relative displacement of the top surface with respect to bottom surface,
(G = 5 x 10 10 Nm -2 ) (5 marks)
QUESTION III
1.
Show that the height to which a liquid rises in a wettable capillary tube of
2𝑇𝑐𝑜𝑠(𝜃) radius r is given by ℎ = 𝜌𝑟𝑔
− 𝑟
3
(5 marks)
2.
Deduce an expression for the excess pressure inside a spherical soap bubble.[Hint: a soap bubble has two surfaces, the inner and the outer)
(5 marks)
3.
A cubical block of wood, 10 cm on a side, floats at the interface between oil and water with its lower surface 1.5 cm below the interface. The density of the oil is 790 kg/m 3 and that of water is 1000 kg/m 3 . The height of the columns of oil and water are 10 cm each. i.
What is the gauge pressure at the upper face of the block? ii.
What is the gauge pressure at the interface between oil and water? iii.
What is the gauge pressure at the lower end of the block?
(5 marks)
QUESTION IV/15 marks
1.
Explain the term viscosity of a fluid. Define the coefficient of viscosity.
Give the dimensions of coefficient of viscosity and its SI units. Deduce the velocity profile for streamline flow of liquid through a capillary of circular cross-section. (10 marks)
2.
3.14x10
-2 cm 3 of a liquid is flowing out per second through a capillary tube of 1 mm radius. Calculate the velocity of the liquid at a point i.
on the axis of the capillary, ii.
adjacent to the wall. (5 marks)
Page 4 of 4