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15th July 2015, 10:13 AM
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Join Date: Apr 2013
Re: WBJEE Physics Question Paper

As you want the WBJEE Physics Question Paper so here I am providing you the details below
WBJEE Physics Question Paper
2011
1. A body floats in water with 40% of its volume outside water. When the same body
floats in oil 60% of its volume remains outside oil. Then relative density of oil is
a) 0.9 b) 1.0 c) 1.2 d) 1.5
2010
2. Three liquids of equal masses are taken in three identical cubical vessels A, B and C.
Their densities are , A B ρ ρ and C ρ respectively but A B C ρ ρ ρ < < . The force exerted by
the liquid on the base of the cubical vessel is
a) Maximum in vessel C b) Minimum in vessel C
c) The same in all the vessels d) Maximum in vessel A
2008
3. A common hydrometer reads specific gravity of liquids. Compared to the 1.6 mark
of the stem the mark 1.5 will be
a) Upwards
b) Downwards
c) In the sample place
d) May be upward or downward depending upon the hydrometer
2006
4. By sucking through a straw a student can reduce the pressure in his lungs to 750 mm
of Hg (density = 3 13.6gcm− ). Using the straw, he can drink water from a glass up to a
maximum depth of
a) 10cm b) 75cm c) 13.6cm d) 1.36 cm
2005
5. From the adjacent figure, the correct observation is
a) The pressure on the bottom of tank A is greater than at the bottom of B
b) The pressure on the bottom of the tank A is smaller than at the bottom of B
c) The pressure depends on the shape of the container
d) The pressure on the bottom of A and B is the same
Pascal’s Law and Archimedes Principle
2010
6. A liquid X of density 3 3.36 / g cm is poured in a U-tube in right arm with height 10cm,
which contains Hg. Another liquid Y is poured in left arm with height 8cm. Upper
levels of X and Y is same. What is the density of Y
a) 0.8 g/cc b) 1.2 g/cc c) 1.4 g/cc d) 1.6 g/cc
2009
7. Assertion (A): A floats higher in the water on a high pressure day than on a low
pressure day.
Reason (R): Floating of ship in the water is not possible because of buoyancy force
which is present due to pressure difference.
a) Both assertion and reason are true and reason is the correct explanation of assertion.
b) Both assertion and reason are true but reason is not the correct explanation of assertion.
c) Assertion is true but reason is false.
d) Both assertion and reason are false.
2008
8. An ice block floats in a liquid whose density is less than water. A part of block is
outside the liquid. When whole of ice has melted, the liquid level will
a) Rise b) Go down
c) Remain same d) First rise then go down
9. A cube made of material having a density of 3 3 0.9 10 kg m− × − floats between water and
a liquid of density 3 3 0.7 10 kg m− × − , which is immiscible with water. What part of the
cube is immersed in water?
a) 1
3
b) 2
3
c) 3
4
d) 3
7
2007
10. Assertion (A): Taking into account the fact that any object which floats must have an
average density less than that of water during world war I, a number of cargo vessels
were made of concrete.
Reason (R): Concrete cargo vessels were filled with air.
a) Both assertion and reason are true and reason is the correct explanation of assertion.
b) Both assertion and reason are true but reason is not the correct explanation of assertion.
c) Assertion is true but reason is false.
d) Both assertion and reason are false.
11. A body floats with one-third of its volume outside water and ¾ of its volume outside
another liquid. The density of the other liquid is
a) 1 9
4
g cc− b) 1 4
0
g cc− c) 1 8
3
g cc− d) 1 3
8
g cc−
2005
12. For a constant hydraulic stress on an object, the fractional change in the object’s
volume ( / ) V V Δ and its bulk modulus (B) are related as
a) V B
V
Δ
∝ b) 1 V
V B
Δ
∝ c) 2 V B
V
Δ
∝ d) 2 V B
V
− Δ

13. A candle of diameter d is floating on a liquid in a cylindrical container of diameter D
(D>>d) as shown in figure. If it’s burning at the rate of 1 2cmh− , then the top of the
candle will
a) Remain at the same height b) Fall at the rate of 1 1cmh−
c) Fall at the rate of 1 2cmh− d) Go up at the rate of 1 1cmh−
Fluid Flow
2009
14. In a streamline flow
a) The speed of a particle always remains same
b) The velocity of a particle always remains same
c) The kinetic energies of all particles arriving at a given point are the same
d) The momentum of all the particle arriving at a given point are the same
2008
15. A rectangular vessel when full of water, takes 10 min to be emptied through an
orifice in its bottom. How much time will it take to be emptied when half filled with
water?
a) 9 min b) 7 min c) 5 min d) 3 min
16. An air bubble of radius 1cm rises from the bottom portion through a liquid of
density 1 1.5 gcc− at a constant speed of 1 0.25cms− . If the density of air is neglected, the
coefficient of viscosity of the liquid is approximately (in Pa).
a) 13000 b) 1300 c) 130 d) 13
17. If the terminal speed of a sphere of gold (density 3 19.5kg m = − ) is 1 0.2ms− in viscous
liquid (density 3 1.5kg ms − ), find the terminal speed of a sphere of silver (density
3 10.5kg ms− − ), of the same size in the same liquid
a) 1 0.4ms− b) 1 0.133ms− c) 1 0.1ms− d) 1 0.2ms−
18. Water is filled in a cylindrical container to a height of 3m. The ratio of the crosssectional
area of the orifice and the breaker is 0.1. The square of the speed of the
liquid coming out from the orifice is 2 ( 10 ) g ms− =
a) 2 2 50m s− b) 2 2 50.5m s− c) 2 2 51m s− d) 2 2 52m s−
19. A uniformly tapering vessel is filled with a liquid of density 3 900kg m − . The force that
acts on the base of the vessel due to the liquid is 2 ( 10 ) g ms− =
a) 3.6 N b) 7.2 N c) 9.0N d) 14.4N
20. To get the maximum flight a ball must be thrown as
a) b) c) d) Any of a, b and c
21. In the figure, the velocity 3 v will be
a) Zero b) 1 4ms− c) 1 1ms− d) 1 3ms−
2007
22. A capillary tube is attached horizontally to a constant head arrangement. If the
radius of the capillary tube is increased by 10%, then the rate of flow of liquid will
change nearly by
a) +10% b) +46% c) -10% d) -40%
23. Two equal drops of water are falling through air with a steady velocity v. If the
drops coalesced what will be the new velocity
a) 1/3 (2) v b) 3/2 (2) v c) 2/3 (2) v d) 1/4 (2) v
24. A good lubricant should have
a) High viscosity b) Low viscosity c) Moderate viscosity d) High density
25. When a body falls in air, the resistance of air depends to a great extent on the shape
of the body. Three different shapes are given. Identify the combination a of air
resistances which truly represents the physical situation (The cross –sectional areas
are the same)
a) 1 < 2 < 3 b) 2 < 3 < 1 c) 3 < 2 < 1 d) 3 < 1 < 2
26. The terminal velocity of small-sized spherical body of radius r falling vertically in a
viscous liquid is given by the following proportionality
a) 2 1/ r b) 1/r c) r d) 2 r
27. The reading of a manometer fitted to a closed tap is 5 2 3.5 10 Nm × . If the value is
opened the reading of the manometer falls to 5 2 3 10 Nm− × . The velocity of water is
a) 1 1ms− b) 1 10ms− c) 1 100ms− d) 1 0.1ms−
28. Speed of a ball of 2cm radius in a viscous liquid is 1 20cms− . Then the speed of 1cm
radius of ball in the same liquid is
a) 1 80cms− b) 1 40cms− c) 1 10cms− d) 1 5cms−
29. A hole is in the bottom of the tank having water. If total pressure at the bottom is 3
atm (1 atm= 5 2 10 Nm− ), then velocity of water flowing from hole is
a) 1 400ms− b) 1 600ms− c) 1 60ms− d) None of these
2006
30. According to Bernoulli’s equation
2 1 constant
2
p v h
g g ρ
+ + = . The terms, A, B and C are
generally called respectively
a) Gravitational Head, Pressure Head and Velocity Head
b) Gravity, Gravitational Head and Velocity Head
c) Pressure Head, Gravitational Head and Velocity Head
d) Gravity, Pressure and Velocity Head
31. Assertion (A): Use of ball bearing, between two moving parts of machine is common
practice.
Reason (R): Ball bearing, reduce vibrations and provide good stability.
a) Both assertion and reason are true and reason is the correct explanation of assertion.
b) Both assertion and reason are true but reason is not the correct explanation of assertion.
c) Assertion is true but reason is false.
d) Both assertion and reason are false.
2005
32. A given shaped glass tube having uniform cross-section is filled with water and is
mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant
angular velocity ω, then
a) Water levels in both sections A and B go up
b) Water level in section A goes up and that in B comes down
c) Water level in section A comes down and that in B it goes up
d) Water levels remain same in both sections
33. Assertion (A): For Reynolds’s number 2000 e R > , the flow of fluid is turbulent.
Reason (R): Inertial forces are dominant compared to the viscous forces at such high
Reynolds’s numbers.
a) Both assertion and reason are true and reason is the correct explanation of assertion.
b) Both assertion and reason are true but reason is not the correct explanation of assertion.
c) Assertion is true but reason is false.
d) Both assertion and reason are false.
34. A container with square base of side a, is filled up to a height H with a liquid. A hole
is made a depth h from then free surface of water. With what acceleration the
container must be accelerated, so that the water does not come out
a) g b)
2
g c) 2
2
gH d) 2gH
a
2004
35. In old age arteries carrying blood in the human body become arrow resulting in an
increase in the blood pressure. This follows from
a) Pascal’s law b) Stoke’s law
c) Bernoulli’s principle d) Archimedes principle
2003
36. A lead shot of a 1mm diameter falls through a long column of glycerine. The
variation of its velocity v with distance covered is represented by
a) b) c) d)
Surface Tension and Surfaces Energy
2004
37. Calculate the force required to separate the glass plate of area 2 2 10 m − with a film of
water 0.05mm thick (surface tension of water is 2 2 10 m − )
a) 25N b) 20N c) 14N d) 28N
Pressure Difference
2010
38. A uniform long tube is bent into a circle of radius R and it lies in vertical plane. Two
liquids of same volume but densities ρand δ fill half the tube the angle θ is
a) 1 tan
ρ δ
ρ δ
− ⎛ ⎞ −
⎜ ⎟ + ⎝ ⎠
b) 1 tan
ρ
δ
− ⎛ ⎞
⎜ ⎟
⎝ ⎠
c) 1 tan
δ
ρ
− ⎛ ⎞
⎜ ⎟
⎝ ⎠
d) 1 tan
ρ δ
ρ δ
− ⎛ ⎞ +
⎜ ⎟ − ⎝ ⎠
2008
39. Two soap bubbles have radii in the ratio of 2: 1. What is the ratio of excess pressures
inside them?
a) 1 :2 b) 1 : 4 c) 2 : 1 d) 4 : 1
40. A water drop is divided into 8 equal droplets. The pressure difference between the
inner and outer side of the big drop will be
a) Same as for smaller droplet b) 1
2
of that for smaller droplet
c) 1
4
of that for smaller droplet d) Twice that for smaller droplet
41. Find the difference of air pressure between the inside and outside of a soap bubble 5
mm in diameter, if the surface tension is 1 1.6Nm−
a) 2 2560Nm− b) 2 3720Nm− c) 2 1208Nm− d) 2 10132Nm−
2004
42. A thread is tied slightly loose to a wire frame as in figure and the frame is dipped
into a soap solution and taken out. The frame is completely covered with the film.
When the portion A is punctured with a pin, the thread
a) Becomes concave towards A
b) Becomes convex towards A
c) Either (a) or (b) depending on the position of A with respect to B
d) Remains in the initial position
2003
43. If the radius soap bubble is four times that of another, then the ratio of their
pressure will be
a) 1 :4 b) 4 : 1 c) 16 : 1 d) 1 : 16
Capillarity
2007
44. If the length of tube is less and cannot accommodate the maximum rise of liquid,
then
a) Liquid will form fountain
b) Liquid will not rise
c) The meniscus will itself so that the water does not spill
d) None of the above
2004
45. What is the shape when a non-wetting liquid is placed in a capillary tube?
a) Concave upwards b) Convex upwards
c) Concave downwards d) Convex downwards
46. In a capillary tube, water rises to 3mm. The height of water that will rise in another
capillary tube having one-third radius of the first is
a) 1mm b) 3mm c) 6mm d) 9mm
Key
1) d 2) c 3) b 4) c 5) d 6) a 7) c 8) b 9) b 10) a
11) c 12) b 13) b 14) c 15) b 16) c 17) c 18) a 19) b 20) b
21) c 22) b 23) b 24) a 25) c 26) d 27) b 28) d 29) a
30) c 31) c 32) d 33) a 34) a 35) c 36) a 37) d 38) a 39) a
40) b 41) a 42) c 43) b 44) c 45) b 46) d
Hints
Pressure and Density
1. 1 0.6 V g V g σ σ = and 2 0.4 V g V g σ σ =
1
2
0.6 1
0.4
σ
σ
=
2
1
6 3
4 2
σ
σ
= = = 1.5
2. Force exerted by the liquid on the base of the vessel is F = mg
But, A B C m m m = =
A B C F F F ∴ = =
4. Pressure difference between lungs of student and atmospheric = (760 – 750) mm of Hg
, hdg = 10 mm of Hg = 1cm of Hg
Or h x 1 = 1 x 13.6
13.6 h cm ∴ =
5. p = hdg
i.e., the pressure depends on the height of liquid column not on its size, so pressure at the
bottom of A and B is same.
Pascal’s Law and Archimedes’ Principle
6. 8 2 10 Y Hg X g g g ρ ρ ρ × × + × × = × ×
8 2 13.6 10 3.36 Y
ρ∴ + × = ×
Or 33.6 27.2
8 r
ρ −
= = 0.8 g/cc
9. Let l = side of the cube
x = side of cube immersed in liquid
l – x = side of cube immersed in liquid
According to law of floating
3 3 2 2 3 0.9 10 ( ) 1000 ( ) 0.7 10 l g l x g l l x g × × × = × × + − × ×
0.9 ( ) 0.7 l x l x × = + − ×
Or 0.3 0.2 x l =
Or 2
3
x
l
=
11. In water weight of body = weight of water displaced 2 1
3
V g = × ×
In another liquid, weight of body 1
4
V g ρ = × × ×
2 1
3 4
Vg V g ρ ∴ =
Or 1 8
3
gcc ρ − =
13. Weight of candle = weight of liquid displaced
i.e., V g V g ρ ρ ′ ′ =
Or
2 2
2
4 4
d d L L π ρ π ρ
⎛ ⎞ ⎛ ⎞
′ × = ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
or 1
2
ρ
ρ
=

Since, candled is burning at the rate of 2cm per hour, then after an hour it will remain 2L –
2 cm
(2 2) ( ) L L x ρ ρ′ ∴ − = −
Or
2( 1)
L x
L
ρ
ρ

=
′ −
So, 1
2 2( 1)
L x
L

=

Or L – 1 = L – X
Or x = 1cm
Thus, it falls at the rate of 1 1 cmh−
15. If 0 A is the area of orifice at the bottom below the free surface and A that of vessel, time t
taken to be emptied the tank
0
2 A H t
A g
=
1 1
2 2
t H
t H
∴ =
1
2 2
H t
t H
⇒ =
2
2 1/ 2
H t
t H
⇒ =
2
2 t
t
⇒ =
2
10 7min
2 2
t t ∴ = = ≈
16. Terminal velocity
2 2
9
r g v ρ
η
=
2 2 .
9
r g
v
ρ
η ⇒ =
2 2 3
2
2 (1 10 ) (1.5 10 ) 9.8
9 0.25 10


× × × ×
=
×
130Pa s = −
17.
2 2 ( )
9 T
r g v ρ σ
η

− =
Where ρ= density of substance of body and
σ= Density of liquid
( )
( )
Ag l T
T glod l
v Ag
v Gold
ρ σ
ρ σ

=

10.5 1.5 9 ( ) 0.2 0.2
19.5 1.5 18 T v Ag −
⇒ = × = ×

1 0.1ms− =
18. av V
A
⇒ =
2 2 1 1 0
2 2
p gh v p v ρ ρ ρ + + = + +
2
2 2
2 2 10 (3 0.525)
1 (0.1)
1
gh v
a
A
× × =
⇒ = =
− ⎛ ⎞ −⎜ ⎟
⎝ ⎠
2 50( / ) m s =
19. Pressure of liquid column h g ρ =
2 0.4 900 10 p Nm− = × ×
Force on the base = p x area 3 2 2 10 p m − = × × 3 0.4 900 10 2 10 N − = × × × × = 7.2N
21. 1 1 2 2 3 3 Av A v A v = +
3 0.2 4 0.2 2 0.4v ∴ × = × +
Or 3 0.4 0.8 0.4 0.4 v = − =
Or 1
3 1 v ms− =
22.
4
8
pr V
l
π
η
=
4 V r ∴ ∝
4
2 2
1 1
V r
V r
⎛ ⎞
⇒ =⎜ ⎟
⎝ ⎠
4
4
2 1 1
110 (1.1)
100
V V V ⎛ ⎞ ∴ = = ⎜ ⎟
⎝ ⎠
= 1.46441V
2 1 V V V
V V
− Δ
∴ = 1.4641V V
V

= = 0.46 or 46%
23.
2 2 ( )
9
r g v ρ σ
η

=
1/3 (2) R r =
1/3 2 2 (2 ) ( )
9
r g v ρ σ
η
⎡ ⎤ − ′ = ⎢ ⎥
⎣ ⎦
2/3 (2) v
v

= or 2/3 (2) v v ′ =
26.
2 2 ( )
9
r g v ρ σ
η

=
So, 2 v r ∝
27. From Bernoulli’s theorem,
2 2
1 1 2 2
1 1
2 2
p v p v ρ ρ + = +
2 2
2 1 2 1
1 1 ( )
2 2
v p p v ρ ρ ⇒ = − +
1 2 ( ) p p = − 1 ( 0) v = ∵
1 2
2
2( ) p p v
ρ

⇒ =
5 5
2 3
2(3.5 10 3 10 )
10
v × − ×
⇒ =
1
2 10 v ms− ⇒ =
28.
2 2 ( )
9
r g v ρ σ
η

=
2 v r ⇒ ∝
Here 1
1 20 v cms− = , 1 2 r cm = , 2 1 r cm =
2
1
2 2
2 2
20 (2)
(1)
v
v r
∴ = =
1
2 20 / 4 5 v cms− ⇒ = =
29. Let height of water column in the tank be h.
Total pressure (p) = atmospheric pressure 0 ( ) p + pressure
Due to water column in tank ( ) p′
0 3 1 2 p p p atm ′ ∴ = − = − =
Or 5 2 10 h g ρ = ×
Or 3 5 10 10 2 10 h× × = ×
Or h = 20m
Velocity of efflux is
2 2 10 20 v gh = = × × 1 400ms− =
30. 2 1 tan
2
p gh v cons t ρ ρ + + =
Dividing this expression by g ρ , we have
2
2
p v h
g g ρ
+ + =Constant
In this expression p
g ρ
is called the pressure head
2
2
v
g
the velocity head and h the
gravitational head
37. 2TA F
d
=
A 2 2 10 m − =
d = 0.05 mm 3 0.05 10 m − = ×
3 2
3
2 70 10 10 28
0.05 10
F N
− −

× × ×
∴ = =
×
38. (cos sin ) (cos sin ) gR gR δ θ θ ρ θ θ + = −
cos sin cos sin δ θ δ θ ρ θ ρ θ = + = −
sin ( ) cos ( ) θ δ ρ θ ρ δ ⇒ + = −
tan
ρ δ
θ
ρ δ

⇒ =
+
39. 4T p
r
=
1 1 2
2 2 1
4 /
4 /
p T r r
p T r r
= =
1
2
1
2
p
p
=
40. Volume of big drop = volume of 8 droplets
3 3 4 4 8
3 3
R r π π = ×
2
R r ∴ =
For smaller drop
2 2 4
/ 2 s
T T T p
r R R
Δ = = =
For bigger drop
2 1
2 s s
T p p
R
Δ = = Δ
41. The excess pressure p of bubble in air is given by
3
4 41.6
2.5 10
T p
R −
×
= =
×
2 2560Nm− =
43. Radius of first bubble 1r R =
Radius of second bubble 2 4 r R =
The pressure of the soap bubble is
4T p
R
=
1 p
R
⇒ ∝
Hence, 1 2
2 1
4 4 :1 p R R
p R R
= = =
1 2 : 4:1 p p =
46. 2 cos T h
r g
θ
ρ
=
1 h
r
⇒ ∝
1 3 h mm = , 1
2 3
r
r =
1 2
2 1
h r
h r
∴ =
2
3 1
3 h
⇒ =
2 9 h mm ⇒ =


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