1. Elasticity &Fluid dynamics
Total No.of questions in Elasticity & Fluid dynamics are -
Level # 1 ....................................................................................41
Level # 2 ....................................................................................32
Level # 3 ....................................................................................14
Level # 4 ....................................................................................23
Total No. of questions ............................................................ 110

2. Q.1 (a) Glass is more elastic than rubber
(b) Rubber is more elastic than glass
(c) Steel is more elastic than rubber
(d) Rubber is more elastic than steel
For the above statements–
(A) (a) and (b) are correct
(B) (a) and (c) are correct
(C) (b) and (c) are correct
(D) (b) and (d) are correct
Q.2 Two similar balls, one of which is made of
ivory while the other, of clay, are dropped
from the same height, then–
(A) the ivory ball will bounce to a greater
height
(B) the caly ball will bounce to a greater
height
(C) both the balls will bounce to the same
height
(D) the ivory ball will not at all bounce
Q.3 Which of the following is not dimension less–
(A) Poisson ratio (B) Sharing strain
(C) Longitudinal strain (D) Volume stress
Q.4 The longitudinal extension of any elastic
material is very small. In order to have an
appreciable change, the material must be in
the form of–
(A) thin block of any cross section
(B) thick block of any cross section
(C) long thin wire
(D) short thin wire
Q.5 The modulus of elasticity of a material does
not depend upon–
(A) shape (B) temperature
(C) nature of material (D) impurities mixed
Q.6 A steel wire is stretched by 1 kg. wt. If the
radius of the wire is doubled, its Young’s
modulus will–
(A) remain unchanged
(B) become half
(C) become double
(D) become four times
Q.7 On withdrawing the applied force on some
objects, the deformity caused gradually
diminishes with time. This is called–
(A) elastic fatigue
(B) elastic limit
(C) coefficient of elasticity
(D) elastic after effect
Q.8 On stretching some substances, permanent
elongation is caused, because–
(A) they are perfectly elastic
(B) they are perfectly plastic
(C) more stress acts on them
(D) their strain is infinite
Q.9 Out of the following whose elasticity is
independent of temperature–
(A) steel (B) copper
(C) invar steel (D) glass
Q.10 A cable that can support a load W is cut into
two equal parts. The maximum load that
can be supported by either part is–
(A)
4
W
(B)
2
W
(C) W (D) 2 W
Q.11 On withdrawing the external applied force on
bodies within the elastic limit, the body–
(A) regains its previous state very quickly
(B) regains its previous state after some time
(C) regain its previous state after a very long
time
(D) does not regain its previous state
Q.12 Elasticity is the property which is caused
by–
(A) the applied deforming forces
(B) gravitational force
(C) nuclear forces
(D) inter-molecular forces
Q.13 The effect of temperature on the value of
Young’s modulus of elasticity for various
substances in general is–
(A) it increases with increase in temperature
(B) remains constant
(C) decrease with rise in temperature
(D) sometimes increases and sometimes
decreases with temperature
LEVEL # 1
ELASTICITY

3. Q.14 The number of independent elastic constants
of a solid is–
(A) 1 (B) 2
(C) 3 (D) 4
Q.15 The ratio of coefficient of isothermal and
adiabatic elasticities of a gas is–
(A)  (B) 2
(C) 1/ (D) 1/2
Q.16 The following four wires are made of the same
material. Which of these will have the largest
extension when the same tension is applied–
(A) length 50 cm and diameter 0.5 mm
(B) length 100 cm and diameter 1 mm
(C) length 100 cm and diameter 2 mm
(D) length 300 cm and diameter 3 mm
Q.17 An iron rod of length  and of cross-section
area A is heated from 0ºC to 100ºC. If the
rod neither expands nor bends, then the
developed F is proportional to–
(A)  (B) 0
(C) –1 (D) A–1
Q.18 When a wire is stretched, an amount of work
is done. What is the amount of work done
in stretching a wire through 0.1 mm, if its
length is 2m and area of cross-section,
10–6m2 (Y = 2 × 1011 N/m2)
(A) 5 × 10–1 J (B) 5 × 10–2 J
(C) 5 × 10–3 J (D) 5 × 10–4 J
Q.19 How many times is the adiabatic modulus of
elasticity of gas as compared to its isothermal
modulus of elasticity–
(A) two times (B) three times
(C)  times (D) 1/ times
Q.20 An iron bar of length  cm and cross section
A cm2 is pulled by a force of F dynes from
ends so as to produce an elongation  cm.
Which of the following statement is correct–
(A) elongation is inversely proportional to
length
(B) elongation is directly proportional to cross
section A
(C) elongation is inversely proportional to A
(D) elongation is directly proportional to
Young’s modulus
Q.21 On abruptly withdrawing the stretching force
acting on a wire, its temperature will–
(A) increase
(B) decrease
(C) remain unchanged
(D) nothing can be stated
Q.22 The ‘’ of a material is 0.20. If a longitudinal
strain of 4.0 × 10–3 is caused, by what
percentage will the volume change–
(A) 0.48 % (B) 0.32 %
(C) 0.24 % (D) 0.50 %
Q.23 A cylinder is of length  and diameter d. On
stretching the cylinder, an increment  in
length and decrease d in diameter are
caused. The Poisson ratio is–
(A)  =
d
d






(B)  =






d
d
(C)  =
d
d






(D)  =
d
d






Q.24 Steel is more elastic than rubber because for
a given load the strain produced in steel as
compared to that produced in rubber is–
(A) more
(B) less
(C) equal
(D) nothing can be said
Q.25 In a wire stretched by hanging a weight from
its end, the elastic potential energy per unit
volume in terms of longitudinal strain  and
modulus of elasticity Y is–
(A) Y 2/2 (B) Y /2
(C) Y 2 (D) Y2 /2
Q.26 The formula for compressibility of a gas is–
(A) PdV/V (B) (1/P) dP/dV
(C) V .
dV
dP
(D)
dP
dV
.
V
1
Q.27 The potential energy of a metallic rod when
it is compressed–
(A) increases (B) remains constant
(C) decreases (D) becomes infinite
FLUID DYNAMICS : BERNOULLI'S THEORY &
EQUATION OF CONTNUITY
Q.28 An incompressible fluid flows steabily through
a cylindrical pipe which has radius 2R at
point A and radius R at point B further along
the flow direction. If the velocity at point A is
, its velocity at point B will be –
(A) 2 (B) 
(C) /2 (D) 4
Q.29 Water is flowing in a horizontal pipe of non-
uniform cross - section. At the most
contracted place of the pipe –
(A) Velocity of water will be maximum and
pressure minimum
(B) Pressure of water will be maximum and
velocity minimum
(C) Both pressure and velocity of water will
be maximum
(D) Both pressure and velocity of water will
be minimum

4. Q.30 Water is flowing in a tube of non-uniform
radius. The ratio of the radii at entrance and
exit ends of tube is 3 : 2. The ratio of the
velocities of water entering in and exiting from
the tube will be –
(A) 8 : 27 (B) 4 : 9
(C) 1 : 1 (D) 9 : 4
Q.31 Water from a tap emerges vertically downward
with an initial speed of 1.0 ms–1. The cross-
section area of the tap is 10–4m2. Assumed
at the pressure is constant throughout the
stream of water and that the flow is steady.
The cross-sectional areal of the stream
0.15 m below the tap is (g = 10 m/s2)
(A) 5.0 × 10–4 m2 (B) 1.0 × 10–5 m2
(C) 5.0 × 10–5 m2 (D) 2.0 × 10–5 m2
Q.32 The velocity of a small ball of mass M and
density d1, when dropped in a container filled
with glycerine becomes constant after some
time. If the density of glycerine is d2, the
viscous force acting on the ball will be –
(A)
2
1
d
g
Md
(B)
g
)
d
d
(
M 2
1 
(C) 








1
2
d
d
1
Mg (D) M d1 d2
Q.33 Bernoulli’s theorem based upon –
(A) Conservation of momentum
(B) Conservation of energy
(C) Conservation mass
(D) None of these
(D) Faraday’s law
Q.34 There is a gale over a house. The force on
the roof of the house due to the gale is –
(A) Directed downward (B) Directed upward
(C) Zero (D) None of these
Q.35 A tank has an orifice near its bottom. The
volume of the liquid flowing per second out of
the orifice does not depend upon –
(A) Area of the orifice
(B) Height of the liquid level above the orifice
(C) Density of liquid
(D) Acceleration due to gravity
Q.36 The rate of flowing of water from the orifice in
a wall of a tank will be more if the orific is –
(A) Near the bottom
(B) Near the upper end
(C) Exactly in the middle
(D) Does not depend upon the position of
orific
Q.37 A tank is filled with water to a height H. A
hole is made in one of the walls at a depth
D below the water surface. The distance x
from the foot of the wall at which the stream
of water coming out of the tank strikes the
ground is given by –
(A) x = 2 [D(H – D)]1/2 (B) x = 2 (gD)1/2
(C) x = 2 [D(H + D)]1/2 (D) None of these
VISCOSITY
Q.38 A small lead ball is falling freely in a viscous
liquid. The velocity of the ball –
(A) goes on increasing
(B) goes on decreasing
(C) remains constant
(D) first increases and then becomes
constant
Q.39 The terminal velocity of a spherical ball of
radius r falling through a viscous liquid is
proportional to –
(A) r (B) r2
(C) r3 (D) r –1
Q.40 The viscous force acting on a solid ball moving
in air with terminal velocity  is directly
proportional to–
(A)  (B) 
(C)

1
(D) 2
Q.41 A small spherical solid ball is dropped in a
viscous liquid. Its journey in the liquid is best
described in the figure by –
(A) Curve A (B) Curve B
(C) Curve C (D) Curve D

5. Q.1 A spherical ball contracts in volume by 0.01%
when subjected to a normal uniform pressure
of 100 atmospheres. The bulk modulus of its
material in dynes/ cm2 is-
(A) 10 × 1012 (B) 100 × 1012
(C) 1 × 1012 (D) 2.0 × 1011
Q.2 When 1 kg wt. is suspended from a wire, the
increment produced is 2 mm, What will be
the increment in lengths when 4 kg wt. is
suspended from it-
(A) 4 mm (B) 8 mm
(C) 0.5 mm (D) 10 mm
Q.3 On increasing temperature, the elasticity of
a material-
(A) decreases
(B) increases
(C) sometimes increases and sometimes
decreases
(D) remains same
Q.4 Two wires, one of copper and the other of
steel, are of same length and cross section.
They are welded together to from a long wire.
On suspending a weight at its one end,
increment in length is found to be 3 cms. If
Young's modulus of steel is double that of
copper, the increment in steel wire will be-
(A) 1 cm (B) 2 cm
(C) 1.5 cm (D) 2.5 cm
Q.5 On mixing impurities, the elasticity of a
material-
(A) decreases
(B) increases
(C) sometimes increases and sometimes
decreases
(D) remains same
Q.6 The bulk modulus of rubber is 9.1 × 108 N/ m2.
To what depth a rubber ball be taken in a
lake so that its volume is decreased by 0.1%?
(A) 1 km (B) 25 m
(C) 100 m (D) 200 m
LEVEL # 2
(ELASTICITY)
Q.7 On applying the load, the increment in length
of a wire is 1 mm. On applying the same
load on another wire of same length and
material, but having half the radius, the
increment will be:
(A) 0.25 mm (B) 4.0 mm
(C) 0.5 mm (D) 2.0 mm
Q.8 Which of the following shows greater
increment in length when subjected to same
load to wires made of same material :
(A) L = 1 m and r = 1 mm
(B) L = 1 m and r = 2 mm
(C) L = 2 m and r = 1 mm
(D) L = 2 m and r = 2 mm
Q.9 The isothermal bulk modulus of a perfect gas
at atmospheric pressure is-
(A) 1.03 × 105 newton/ m2
(B) 1.03 × 104 newton/ m2
(C) 1.03 × 1010 newton/ m2
(D) 1.03 × 1011 newton/ m2
Q.10 Two rods A and B of the same material and
length have their radii r1 and r2 respectively.
when they are rigidly fixed at one end and
twisted by the same couple applied at the
other end, the ratio








B
of
end
the
at
twist
of
angle
the
A
of
end
the
at
twist
of
angle
the
is-
(A) 2
1
r / 2
2
r (B) 3
2
3
1 r
/
r
(C) 4
1
4
2 r
/
r (D) 4
2
4
1 r
/
r
Q.11 An metal rod of Young's modulus
2 × 1010 newton/ metre2, undergoes an
elastic strain of 0.06%. The energy per unit
volume stored in joule/metre2 is-
(A) 3600 (B) 7200
(C) 1800 (D) 900
Q.12 The compressibility of water is 4 × 10–5 per
unit atmospheric pressure. The decreased
volume of 100 cm3 of water under a pressure
of 100 atmosphere will be-
(A) 0.4 cm3 (B) 4 × 10–5 cm3
(C) 0.025 m3 (D) 0.004 cm3
Q.13 The Young's modulus and strain for steel at
the breaking point are 2 × 1011 N/m2 and
0.15 respectively. Hence the stress at the
breaking point in newton/ m2 for steel will be-
(A) 1.33 × 1011 (B) 1.33 ×1010
(C) 3 × 109 (D) 3 × 1010

6. Q.14 The force constant between the restoring
force F and displacement x of a spring
according to the graph shown will be-
(A) 3 (B) 3 /2
(C) 1/2 (D) 1/ 3
Q.15 If a stretching force F1 is applied on a vertical
metal wire then its length is L1 and if force
F2 is applied on it then its length becomes
L2. The real length of wire is-
(A)
1
2
1
2
2
1
F
F
L
F
L
F


(B)
1
2
2
1
1
2
F
F
L
F
L
F


(C)
2
L
L 2
1 
(D) 2
1L
L
Q.16 A metal rod of length , area of cross section
A, Young's modulus Y, and thermal linear
coefficient of expansion  is clamped at both
of its ends. If it is heated through t°C, the
force acting on the rod is-
(A) YAt (B) YAt
(C) YAt/ (D) YAt
Q.17 Poisson's ratio of a certain material is 0.2 .
If a longitudinal strain of 4 × 10–3 is produced
in a uniform rod or this material, the
percentage change in its volume will be-
(A) 0.24% (B) 0.32%
(C) 0.48% (D) 0.56%
Q.18 Steel ring of radius r and cross- section A is
to be mounted on a wooden well. If the
Young's modulus of steel is Y, then the
minimum tensile force required to be
developed in the ring so that it can easily get
mounted on the well will be-
(A)
r
YAR
(B)
R
YAr
(C)
Ar
)
r
R
(
Y 
(D)
r
)
r
R
(
YA 
Q.19 After suspending a body of mass 1 kg from
a wire of negligible mass, length 1 m and
radius 1 mm it is made to oscillate along the
length in a vertical plane. Its frequency is
found to be 100 per s. Young's modulus of
elasticity of the material of wire is-
(A) 1.05 × 1011 N/m2
(B) 1.26 × 1011 N/ m2
(C) 2. 12 × 1011 N/ m2
(D) 2.84 × 1011 N/m2
Q.20 On suspending a weight Mg, the length  of
elastic wire and area of cross- section A, its
length becomes double the initial length. The
instantaneous stress action on the wire is-
(A) Mg/A (B) Mg /2A
(C) 2Mg/ A (D) 4 Mg/A
FLOW OF FLUID & BERNOULLI'S THEORY &
EQUATION OF CONTNUITY
Q.21 Velocity of flow of water in a horizontal pipe
is 10.0 m/s. Find the velocity- head or water
(g = 10.00 m/s2)
(A) 9.00 m (B) 5.00 m
(C) 3.00 m (D) None of these
Q.22 Water is flowing through a cylindrical pipe of
cross- section area 0.09  m2 at a speed of
1.0 m/s. If the diameter of the pipe is halved,
then find the speed of flow of water through
it-
(A) 4.0 m/s (B) 6.0 m/s2
(C) 4.0 m/s2 (D) 6.0 m/s
Q.23 Water is flowing through a horizontal tube of
non- uniform cross- section. At a place the
radius of the tube is 0.5 cm and the velocity
of water there is 20 cm/s. What will be the
velocity at another place where the radius of
the tube is 1.0 cm?
(A) 3 cm/s (B) 7 cm/s
(C) 5 cm/s (D) 0.5 cm/s
Q.24 Water is flowing in a horizontal pipe of non-
uniform area of cross- section. The velocity
of water at a place, where the radius of pipe
is 0.01 m is 25 m/s. What will be the velocity
of water where the radius of pipe is 0.02 m?
(A) 7.25 m/s (B) 6.75 m/s
(C) 6.25 m/s (D) None of these
length have their radii r1
F
x
300

7. Q.25 Water is flowing through a horizontal pipe of
non- uniform cross- section. The speed of
water is 30 cm/s at a place where pressure
is 10 cm(of water). Calculate the speed of
water at the other place where the pressure
is half of that of the first place-
(A) 100.4 cm/s (B) 101.4 cm/s
(C) 102.4 cm/s (D) 103.4 cm/s
Q.26 Water enters a horizontal pipe of non- uniform
cross-section with a velocity of 0.5 m/s and
leaves the other end with a velocity of 0.7 m/s.
The pressure of water at the first end is
103 N/m2. Calculate pressure at the other
end. (Density of water = 1.0 × 103 kg/m3)-
(A) 980 N/m2 (B) 880 N/m2
(C) 800 N/m (D) None of these
Q.27 A water tank has a hole in its wall at a
distance of 40 m below the free surface of
water. Compute the velocity of flow of water
from the hole. If the radius of the hole is
1 mm., find the rate of flow of water-
(A) 26 m/s , 8.8 × 10–5 m3/s
(B) 28 m/s, 8.8 × 10–5 m3/s
(C) 28 m/s, 6.8 × 10–5 m3/s
(D) 26 m/s, 9.8 × 10–5 m3/s
Q.28 The relative velocity between two parallel
layers of water is 8 cm/s and the
perpendicular distance between them is
0.1 cm. Calculate the velocity- gradient-
(A) 90/s (B) 80.5 /s
(C) 80 /s. (D) None of these
Q.29 There is a 1 mm thick layer of oil between a
flat plate of area 10–2 m2 and a big plate.
How much force is required to move the plate
with a velocity of 1.5 cm/s2? The coefficient
of viscosity of oil is 1 poise-
(A) 1.5 × 10–3 N (B) 1.3 × 10–5 N
(C) 1.5 × 10–2 N (D) 1.5 × 102 N
Q.30 A steel shot of diameter 2 mm is dropped in
a viscous liquid filled in a drum. Find the
terminal speed of the shot. Density of the
material of the shot = 8.0 × 103 kg/m3,
density of liquid = 1.0× 103 kg/ m3. Coefficient
of viscosity of liquid = 1.0 kg/(m-s), g= 10 m/s2
(A) 1.55 cm/s (B) 1.455 cm/s
(C) 5.1 cm/s (D) None of these
Q.31 An air bubble (radius 0.4 mm) rises up in
water. If the coefficient of viscosity of water
be 1 × 10–3 kg/(m–s), then determine the
terminal speed of the bubble density of air is
negligible-
(A) 0.843 m/s (B) 3.048 m/s
(C) 0.483 m/s (D) 0.348 m/s
Q.32 If an oil drop of density 0.95 × 103 kg/ m3
and radius 10–4 cm is falling in air whose
density is 1.3 km/m3 and coefficient of
viscosity is 18 × 10–6 kg/(m–s). Calculate
the terminal speed of the drop.
(A) 0.00015 cm/s
(B) 0.0005 cm/s
(C) 0.0115 cm/s
(D) None of these

8. LEVEL # 3
Q.1 The terminal velocity of a ball in air is v, where
acceleration due to gravity is g. Now the same
ball is taken in a gravity free space where all
other conditions are same. The ball is now
pushed at a speed vv, then –
(A) The terminal velocity of the ball will be v/2
(B) The ball will move with a constant velocity
(C) The initial acceleration of the ball is 2g in
opposite direction of the ball's velocity
(D) The ball will finally stop (Given that density
of the ball  = 2 times the density of air )
Q.2 A tank is filled up to a height 2H with a liquid
and is placed on a platform of height H from
the ground. The distance x from the ground
where a small hole is punched to get the
maximum range R is –
(A) H (B) 1.25 H
(C) 1.5 H (D) 2H
Q.3 In a cylindrical vessel containing liquid of
density , there are two holes in the side walls
at heights of h1 and h2 respectively such that
the range of efflux at the bottom of the vessel
is same. The height of a hole, for which the
range of efflux would be maximum, will be –
(A) h2 – h1 (B) h2 + h1
(C)
2
h
h 1
2 
(D)
2
h
h 1
2 
Q.4 Two drops of same radius are falling through
air with steady speed v. If the two drops
coalesce, what would be the terminal speed –
(A) 4v (B) 2v
(C)3v (D) None of these
Q.5 A large tank is filled with water (density =
103 kg/m3). A small hole is made at a depth
10m below water surface. The range of water
issuing out of the hole is R on ground. What
extra pressure must be applied on the water
surface so that the range becomes 2R
(take 1 atm = 105 Pa and g = 10 m/s2) :
(A) 9 atm (B) 4 atm (C) 5 atm (D) 3 atm
Q.6 A ball of relative density 0.8 falls into water
from a height of 2m. The depth to which the
ball will sink is (neglect viscous forces) –
(A) 8m (B) 2 m
(C) 6m (D) 4 m
Q.7 When tension in a metal wire is T1, its length
was l1 and when tension is T2, the length is
l2. Its unstretched length is –
(A) 2
1l
l
(B)
2
2
1 l
l 
(C)
1
2
1
2
2
1
T
T
)
T
T
(

 l
l
(D)
2
1
2
1
2
1
T
T
T
T

 l
l
Q.8 When a sphere is taken to bottom of sea 1 km
deep, it contracts by 0.01%. The bulk modulus
of elasticity of the material of sphere is :
(Given Density of water = 1g/cm3)
(A) 9.8 × 1010 N/m2
(B) 10.2 × 1010 N/m2
(C) 0.98 × 1010 N/m2
(D) 8.4 × 1010 N/m2

9. Passage # 1
Fig shows a bar of uniform cross-section of
area s. Equal and opposite tensile forces are
applied at the ends of the bar. Each force has
a magnitude F. ABCD is a plane through the
bar and inclined at angle  with the
perpendicular to the length of the bar.
F F
D
C
A
B

Answer the following questions : (9 to 11)
Q.9 Normal stress at the plane which is inclined
with the plane perpendicular to the length of
the bar is -
(A) F/s (B) Fcos/s
(C) Fcos2/s (D) F/scos
Q.10 Shear stress on the plane which is inclined
with the plane perpendicular to the length of
the bar is
(A) Fsin/s (B) F/s cos
(C) Ftan/s (D) Fsin2/2s
Q.11 Shear stress on the s aid plane will be
maximum for =
(A) 90° (B) 45°
(C) 30° (D) 0°
Passage # 2 (12 to 14)
A U-tube of base length L contains a liquid of
density  in it. The tube is rotated about one of
its vertical end with angular velocity  as
shown. The diameter of the tube is negligible.
Take P0 as atmospheric presure.
h0
h1
h2
L
A B

Answer the following questions : -
Q.12 What is the force at B due to rotations of the
u-tube ?
(A) A 2
(B) A 2L2
(C)
2
L
A 2
2

(D)
4
L
A 2
2

Q.13 What is the presure at B from left hand side.
(A) P0 + h1 g
(B) P0 +
2
g
h1 
(C) 2P0 + h1 g
(D) P0 + h1 g +
2
L2
2

Q.14 The value of h0 is -
(A)
g
2
L
2

(B)
g
2
L2
2

(C)
g
3
L2
2

(D)
g
4
L2
2


10. LEVEL # 4
[PREVIOUSLY ASKED QUESTIONS IN AIEEE & IIT]
Section - A
Q.1 A wire suspended vertically from one of itsends
is stretched by attaching a weight of 200 N to
the lower end. The weight stretches the wire by
1 mm. Then the elastic energy stored in the
wire is –
(A) 10 J (B) 20 J
(C) 0.1 J (D) 0.2J
Q.2 A spring of spring constant 5 × 103
N/m is
stretched initially by 5 cm from the unstretched
position. Then the work required to stretch it
further by another 5 cm is –
(A) 18.75 N-m (B) 25.00 N-m
(C) 6.25 N-m (D) 12.50 N-m
Q.3 A wire fixed at the upper end stretched by length
 by applying a force F. The work done in
stretching is –
(A) 2F (B) F
(C)

2
F
(C)
2
F
Q.4 If 'S' is stress and 'Y' is Young's modulus of
material of a wire, the energy stored in the wire
per unit volume is
(A) 2S2Y (B)
Y
2
S2
(C) 2
S
Y
2
(D)
Y
2
S
Q.5 A wire elongates by  mm when a load W is
hanged from it. If the wire goes over a pulley
and two weights W each are hung at the two
ends, the elongation of the wire will be (in mm)–
(A) zero (B) /2
(C)  (D) 2
(ELASTICITY)
Q.6 Two wires are made of the same material and
have the same volume. Howerver wire 1 has
cross-section area A and wire 2 has
cross-section area 3A. If the length of wire 1
increases by x on applying force F, how much
force is needed to stretch wire 2 by the same
amount ?
(A) F (B) 4 F
(C) 6 F (D) 9 F
Section - B
Q.1 A highly rigid cubical block of small mass M
and side L is fixed rigidly on to another
cubical block B of the same dimensions and
of low modulus of rigidity  such that the
lower face of A completely covers the upper
face of B. The lower face of B is rigidly held
on a horizontal surface. A small force F is
applied perpendicular to one of the side faces
of A. After the force is withdrawn, block A
executes small oscillations, the time period
of which is given by -
(A) 2 L
M (B) 2 L
/
M
(C) 2 
/
ML (D) 2 L
/
M 
Q.2 A uniform rod of length L and density  is
being pulled along a smooth floor with a
horizontal acceleration (see figure). The
magnitude of the stress at the transverse
cross-section through the mid-point of the
rod is

L
(A) (1/2L) (B) (1/4L)
(C) (1/8L) (D) (L)

11. Q.3 One end of a long metallic wire of length L
is tied to the ceiling. The other end is tied to
a massless spring of spring constant K. A
mass m hangs freely from the free end of
spring. The area of cross-section and the
Young's modulus of the wire are A and Y
respectively. If the mass is slightly pulled
down and released, it will oscillate with a
time period T equal to -
(A) 2
m
K
(B) 2
m YA KL
YAK
( )

(C) 2
mYA
KL
(D) 2
mL
YA
Q.4 A weight W is suspended through a rope of
length 1 m and cross-sectional area 10-6 m2
from a rigid support. The relation between
change in length of rope l & W is shown in
the graph. The young’s Modulus of elasticity
is :
(A) 2×10-5 (B) 2×1011
(C) 5×104 (D) 5×1010
(FLUID DYNAMICS)
Section - A
Q.1 A cylinder of height 20 m is completely filled
withwater.The velocityof efflux of water(inms–1
)
through a small hole on the side wall of the
cylinder near its bottom is – (A)
10 m/s (B) 20 m/s
(C) 25.5 m/s (D) 5 m/s
Q.2 Which one of the following representsthecorrect
dimensionsof the coefficient of viscosity ?
(A) ML–1
T–1
(B) MLT–1
(C) ML–1
T–2
(D) ML–2
T–2
Q.3 Spherical ballsof radius‘R’arefalling in aviscous
fluid of viscosity ‘’ with a velocity ‘v’. The
retarding viscous force acting on the spherical
ball is –
(A) inversely proportional to both radius ‘R’ and
velocity ‘v’
(B) directly proportional to both radius ‘R’ and
velocity ‘v’
(C) directly proportional to ‘R’ but inversely
proportional to ‘v’
(D) inversely proportional to ‘R’ but directly
proportional to velocity ‘v’
Q.4 A 20 cm long capillary tube is dipped in water.
The water rises upto 8 cm. If the entire
arrangement is put in a freely falling elevator
the length of water column in the capillary tube
will be
(A) 8 cm (B) 10 cm
(C) 4 cm (D) 20 cm
Q.5 If the terminal speed of a sphere of gold (densit
y = 19.5 kg/m3) is 0.2 m/s in a viscous liquid
(density = 1.5 kg/m3), find the terminal speed of
a sphere of silver (density = 10.5 kg/m3) of the
same size in the same liquid–
(A) 0.1 m/s (B) 0.2 m/s ( C )
0.4 m/s (D) 0.133 m/s
Q.6 A jar is filled with two non-mixing liquids 1 and 2
having densities 1
and 2
, respectively. Asolid
ball, made of a material of density 3
, isdropped
in the jar. It comes to equilibrium in the position
shown in the figure.Which of the following istrue
for 1
, 2
and 3
?
Liquid 1 

Liquid 2 
(A) 1
> 3
> 2
(B) 1
< 

(C) 1
< 

(D) 3
< 
2

12. Q.7 A spherical solid ball of volume V is made of a
material of density 1
. It is falling through a
liquid of density 2
(2
< 1
). Assume that the
liquid applies a viscous force on the ball that is
proportional to the square of its speed , i.e.,
Fviscous
= – k2
(k > 0). The terminal speed of the
ball is
(A)
k
Vg 1

(B)
k
Vg 1

(C)
k
)
(
Vg 2
1 


(D)
k
)
(
Vg 2
1 


Section - B
Q.1 A tube of length L is filled completely with an
incompressible liquid of mass M and closed
at both the ends. The tube is then rotated in
a horizontal plane about one of its ends with
a uniform angular velocity . The force exerted
by the liquid at the other end is –
(A)
2
L
M 2

(B) M2L
(C)
4
L
M 2

(D)
2
L
M 2
2

.
Q.2 A horizontal pipeline carries water in a
streamline flow. At a point along the pipe
where the cross-sectional area is 10 cm2,
the water velocity is 1 m s–1 and the pressure
is 2000 Pa. The pressure of water at another
point where the cross-sectional area is 5 cm2
is
(Density of water = 103 kg m–3)
(A) 500 Pa (B) 1000 Pa
(C) 250 Pa (D) 750 Pa
Q.3 Water from a tap emerges downwards with
an initial speed of 1.0 ms–1. The cross-
sectional area of the tap is 10–4m2. Assume
that the pressure is constant throughout the
stream of water, and the flow is steady. the
cross-section area of the steam 0.15m below
the tap is : (A) 5.0 ×
10–4 m2 (B) 1.0 × 10–5m2
*(C) 5.0 × 10–5 m2 (D) 2.0 × 10–5 m2
Q.4 A large open tank has two holes in the wall.
One is a square hole of side L at a depth
y from the top and the other is a circular hole
of radius R at a depth 4y from the top. When
the tank is completely filled with water, the
quantities of water flowing out per second
from both holes are the same. Then, R is
equal to - (A)

2
L
(B) 2L (C) L
(D)

2
L
.
Q.5 A vessel filled with water upto height 3m.
There is a hole at height 52.5 cm from the
bottom. Ratio of area of cross section of hole
to vessel is 0.1. Then square of velocity of
the water coming out of hole in (m/s)2
(A) 50 (B) 50.5
(C) 51 (D) 40
Q.6 STATEMENT – 1
The stream of water flowing at high speed
from a garden hose pipe tends to spread like
a fountain when held vertically up, but tends
to narrow down when held vertically down.
and
STATEMENT – 2
In any steady flow of an incompressible fluid,
the volume flow rate of the fluid remains
constant.
(A) STATEMENT – 1 isTrue, STATEMENT- 2
is True; STATEMENT -2 is a correct
explanation for STATEMENT -1
(B) STATEMENT – 1 isTrue, STATEMENT- 2
is True; STATEMENT -2 is NOT a correct
explanation for STATEMENT -1
(C) STATEMENT-1 isTrue, STATEMENT-2 is
False
(D) STATEMENT-1 is False, STATEMENT-2
is True

13. ANSWER KEY
LEVEL # 1
LEVEL # 2
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. B A D C A A A B C C B D C B C A B C C C
Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Ans. B C B B A D C D A B C C B B C A A D B B
Q.No. 41
Ans. C
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Ans. C B A A C C B C A C A A D D B B A D B C
Q.No. 21 22 23 24 25 26 27 28 29 30 31 32
Ans. B A C C D B B C C A D C
LEVEL # 3
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Ans. D C D A D A C A C D B C D D
LEVEL # 4
ELASTICITY
SECTION-A
SECTION-B
Q.No. 1 2 3 4
Ans. D A B B
FLUID DYNAMICS
SECTION-A
SECTION-B
Q.No. 1 2 3 4 5 6 7
Ans. B C B D A C D
Q.No. 1 2 3 4 5 6
Ans. A A C A A A
Q.No. 1 2 3 4 5 6
Ans. C A D B C D