R. K. Academy Lonawala JEE -2014

R. K. Academy Lonawala JEE -2014
Properties Of Matter : Friction in Solids n Liquids [11th], Elasticity, Surface Tension
1.
The Poisson’s ratio of a material is 0.4. If a force is applied to a wire of this material, there is a decrease of crosssectional are a by 2%. The percentage increase in its length is
(1) 3%
(2) 2.5%
(3) 1%
(4)
0.5%
2.
The elongation of a spring of length L and of negligible mass due to a force is x. The spring is cut into two pieces of
lengths in ratio 1 : n. The ratio of the respective spring constants is
(1) n : 1
(2) 1 : n
(3) n2 : 1 (4)
1 : n2
3.
A 60 m3 cube has bulk modulus 1011 pascal. If the pressure P changed to 2 × 107 pascal the change in volume is
(1) –43.2 m3
4.
(2) –43.2 mm3
(3) –43.2 cm3
(4)
–432 mm3
An aluminium wire and steel wire of the same length and cross-section are joined end to end. The composite wire is
20
hung from a rigid support and a load is suspended from the free end. The Young’s modulus of steel is times the Al.
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The ratio of increase of length of Steel to Aluminium is
(1)
20
(2)
7
400
49
(3)
7
20
(4)
49
400
5.
If the work done in stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of same material
but double radius of cross-section and half the length by 1 mm in joule is
(1) 16
(2) 8
(3) 4
(4)
1/4
6.
If a gas is heated at constant pressure, its isothermal compressibility
(1) remains constant
(2) increases linearly with temperature
(3) decreases linearly with temperature
(4) decreases inversely with temperature
7.
A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to
(1) Y2
(2) Y
(3) 1/Y
(4)
1/Y2
8.
A long string is stretched by 2 cm and the potential energy is V. If the spring is stretched by 10 cm, its potential
energy will be
(1) V/25
(2) V/5
(3) 5 V
(4)
25 V
9.
An Indian rubber cord L metre long and area of cross-section A metre2 is suspended vertically. Density of rubber is
kg/m3 and Young’s modulus of rubber is Y n/m2. If the cord extends by l metre under its own weight, then extension
l is
(1)
L2 g / Y
(2)
L2 g / 2Y
(3)
L2 g / 4Y
(4)
Y / L2 g
10. For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section
and circular cross-section is
(1) 3 : π
(2) π: 3
(3) 1 : π
(4)
π:1
11. If there were a smaller gravitational effect, which of the following forces do you think would alter in some respect ?
(1) Viscous forces
(2) Archimede’s uplift
(3) Electrostatic forces
(4) Nuclear forces
12. We go up in the atmosphere in a balloon upto a height of about 40 km and note the temperature. Which of the
following statements is correct?
(1) The temperature will go on falling with altitude continuously
(2) The temperature will go on rising continuously with altitude
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(3) The temperature will go on falling and at a certain height it will reach practically a constant temperature and it
will not change with further increase in height
(4) The temperature will go on falling and at a certain height it will become practically constant with further increase
in height, the temperature rises again
13. In making an alloy, a substance of specific gravity s1 and mass m1 is mixed with another substance of specific gravity
s2 and mass m2, then the specific gravity of the alloy is
(1)
 m1  m2 


 s1  s2 
(2)
 s1s2 


 m1  m2 
(3)


 m1  m2
 m1 m2


 s1 s2






(4)
 m1 m2 



 s1 s2 
 m1  m2 




14. A tank is filled with water upto a height H. Water is allowed to come out of a hole P in one of the walls at a depth h
below the surface of water. Express the horizontal distance x in terms of H and h
(1)
(2)
(3)
(4)
x  h( H  h)
h
x  [h( H  h) / 2]
x  2 h( H  h)
P
H
x  4 h( H  h)
x
15. When a large bubble rises from the bottom of a lake to the surface, its radius doubles. The atmospheric pressure is
equal to that of a column of water of height H. The depth of the lake is
(1) H
(2) 2 H
(3) 7 H
(4)
8H
16. The reading of a spring balance when a block is suspended from it in air is 60 newton. This reading is changed to 40
newton when the block is submerged in water. The specific gravity the block must be therefore,
(1) 3
(2) 2
(3) 6
(4)
3/2
17. In rising from the bottom of a lake to the top, the temperature of an air bubble remains unchanged, but its diameter
gets doubled. If h is the barometric height (expressed in metres of mercury of relative density ρ) at the surface of the
lake, the depth of the lake is
(1) 8ρhm
(2) 4ρhm
(3) 7ρhm
(4) 2ρhm
18. A small cylinder of 2 cm diameter is connected to a large cylinder of 20 cm diameter and each cylinder is fitted with
suitable pistons. An incompressible fluid is filled in the cylinders. If a force of 60 N is applied to the piston of the
small cylinder, then the force exerted on the piston of the large cylinder will be
(1) 12,000 N
(2) 6,000 N
(3) 1,200 N
(4)
600 N
19. The total weight of a piece of wood is 6 kg. In the floating state in water its (1/3) part remains inside the water. On
this floating solid, what maximum weight is to be put such that the whole of the piece of wood is to be drowned in
the ratio?
(1) 12 kg
(2) 10 kg
(3) 14 kg
(4)
15 kg
20. A pump motor delivers 10 kg of water at a certain rate of 1 Lt/s. The rate of flow increase to 2 Lt/s. In order to hold
the pump, the power has to be increased
(1) by four times in the forward direction
(2) by four times in the backward direction
(3) by eight times in the backward direction
(4) twice the original value in forward direction
21. A concrete sphere of radius R has cavity of radius r which is packed with saw dust. The specific gravity of concrete
and saw dust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water. Ratio
of mass of concrete to mass of saw dust will be
(1) 8
(2) 4
(3) 3
(4)
0
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22. Once a submarine starts sinking, it will always sink to the bottom of the ocean if no other changes are made. This is
because during the descent of the submarine
(1) the buoyant force acting on it decreases
(2) the hydrostatic pressure acting on it increases
(3) the gravitational force acting on it increases
(4) its density remains constant
23. A hemispherical bowl just floats without sinking in a liquid of density 1.2 × 103 kg m–3. If outer diameter and the
density of the bowl are 1 m and 2 × 104 kg m–3 respectively, then the inner diameter of the bowl will be
(1) 0.94 m
(2) 0.97 m
(3) 0.98 m
(4)
0.99 m
24. A body when placed in water, floats in it completely immersed. The volume of the body is 100 cm3. It is placed in a
jar. The mass of the jar and water is 400 gm. After placing the body in it, the total mass will be
(1) 250 gm
(2) 400 gm
(3) 300 gm
(4)
500 gm
25. A glass bulb contains air at one atmosphere and 27ºC. The maximum pressure which the bulb can withstand is 2
atmosphere. The temperature at which it will burst is
(1) 27ºC
(2) 54ºC
(3) 327ºC
(4)
600ºC
26. Droplets of a liquid are usually more spherical in shape than larger drops of the same liquid because
(1) Force of surface tension is equal and opposite to the force of gravity
(2) Force of surface tension predominates the force of gravity
(3) Force of gravity predominates the force of surface tension
(4) Force of gravity and force of surface tension act in the same direction and are equal
27. There is a horizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside
the loop and the thread becomes a circular loop of radius R. If the surface tension of the loop be T, then what will be
the tension in the thread
(1) πR2/T
(2) πR2T
(3) πR2T
(4)
RT
28. Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by 75
× 10–4 N force due to the weight of the liquid. If the surface tension of water is 6 × 10–2 Nm–1, the inner
circumference of the capillary must be
(1) 1.25 × 10–2 m
(2) 0.50 × 10–2 m
(3) 6.5 × 10–2 m (4)
12.5 × 10–2 m
29. What change in surface energy will be noticed when a drop of radius splits up into 1000 droplets of radius r. Surface
tension is T
(1) 4πR2T
(2) 7πR2T
(3) 16πR2
(4)
36πR2T
30. Two spherical soap bubble of radii r1 and r2 in vacuum coalesce under isothermal conditions. The resulting bubble
has a radius R such that
(1) R = (r1 + r2)/2
𝑟 𝑟
(2) R = 𝑟 1+𝑟2
1
2
(3) R = 𝑟12 + 𝑟22
(4)
R = r1 + r2
31. Two water droplets merge with each other to form a larger droplet. In this process
(1) Energy is liberated
(2) Energy is absorbed
(3) Energy is neither liberated nor absorbed (4) Some mass is converted into energy
32. By inserting a capillary tube upto a depth t in water, the water rises to a height h. If the lower end of the capillary is
closed inside water and the capillary is taken out and closed end opened, to what height the water will remain in the
tube? Here l > h
(1) zero
(2) l + h
(3) 2 h
(4)
h
33. Under a constant pressure head, the rate of flow of orderly volume flow of liquid through a capillary tube is V. If the
length of the capillary is doubled and the diameter of the bore is halved, the rate of flow would become
(1) V/4
(2) 16 V
(3) V/8
(4)
V/32
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R. K. Academy Lonawala JEE-2014 Regular
34. 16 cm3 of water flows per second through a capillary tube of radius a cm and of length l cm when connected to a
pressure head of h cm of water. If a tube of the same length and radius a/2 cm is connected to the same pressure
head, the quantity of water flowing through the tube per second will be
(1) 16 cm3
(2) 4 cm3
(3) 1 cm3
(4)
8 cm3
35. An incompressible fluid flows steadily through a cylindrical pipe which has radius 2 R at point A and radius R at
point B further along the flow direction. If the velocity at point A is v, its velocity at a point B will be
(1) 2 v
(2) v
(3) v/2
(4)
4v
36. Excess of pressure in a soap bubble of diameter 10 mm when the surface tension is 0.04 N/m is
(1) 16 Pa
(2) 32 Pa
(3) 4 Pa
(4)
64 Pa
37. A long cylindrical glass vessel has a small hole of radius r at its bottom. The depth of which the vessel can be
lowered vertically in a deep water bath (surface tension T ) without any water entering inside is
(1)
𝑇
(2)
𝑟𝑑𝑔
3𝑇
(3)
𝑟𝑑𝑔
2𝑇
(4)
𝑟𝑑𝑔
4𝑇
𝑟𝑑𝑔
38. The terminal velocity vT of a small steel ball of radius r falling under gravity through a column of a viscous liquid of
coefficient of viscosity depends on mass of the ball m, acceleration due to gravity g, coefficient of viscosity and
radius r. Which of the following relations is dimensionally correct?
𝑚𝑔𝑟
𝑚𝑔
𝑚𝑔𝜂
(1) 𝑉𝑇 ∝
(2) 𝑉𝑇 ∝ 𝑚 𝑔 η 𝑟
(3) 𝑉𝑇 ∝
(4) 𝑉𝑇 ∝
𝜂
𝑟𝜂
𝑟
39. A fluid of density d and viscosity η is flowing with an average velocity v measured over the cross-section of a pipe of
radius r. The Reynold’s number R is then given by
(1) 𝑅 =
2𝑟𝑣𝑑
𝜂
(2) 𝑅 =
𝑟𝑣𝑑
𝜂2
(3) 𝑅 =
𝑟𝑣𝑑
𝜂
(4)
𝑅=
2𝑟𝜂
𝑑
40. Two hail stones with radii in the ratio of 1 : 2 fall from a great height through the atmosphere. Then the ratio of their
momenta after they have attained terminal velocity is
(1) 1 : 1
(2) 1 : 4
(3) 1 : 16
(4)
1 : 32
41. A bimetallic strip consists of metals X and Y. It is mounted rigidly at the base as shown. The metal X has a higher
coefficient of expansion compared to that for metal Y. When the bimetallic strip is placed in a cold bath:
(1) It will bend towards the right
(2) It will bend towards the left
(3) It will not bend but shrink
(4) It will neither bend nor shrink
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