Sri Chaitanya IIT Academy
25-12-2021_Jr.Super60_Jee-Main_WTM-18_Q.P
PHYSICS
Max Marks: 100
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its
answer, out of which ONLY ONE option can be correct.
Marking scheme: +4 for correct answer, 0 if not attempted and –1 in all other cases.
1.
2.
A vessel contains oil over mercury. A homogeneous sphere floats with half volume
immersed in mercury and the other half in oil. If density of oil is 0.8 gm/cm3 and that
of mercury is 13.6 gm/cm3. what is the density of material of sphere
1) 6.2 gm/cm3
2) 7.2 gm/cm3
3) 8.2 gm/cm3
4) 9.2 gm/cm3
The tension in a string holding a solid block below the surface of a liquid (of density
greater than that of solid)as shown in figure is T0 when the system is at rest. What
will be the tension in the string if the system has upward acceleration a ?
a
a
3.
1)
4
3
 3 R M

M


3) h
4.

a

a
1) T0  
2) T0 1  
3) T0 1  
4) T0 1  
 a
g
 g
 g
A rubber ball with a mass M and radius R is submerged into a liquid of density to a
depth h and released. What height will the ball jump up above the surface of water?
(Neglect resistance of water and air) (assume h >> R)
g


h


 4 R3 
2) 
h
3 M 
4)
h
2
A uniform rod of length b capable of turning about its end which is out of water rests
inclined to the vertical. If its specific gravity is 5/9,find the length immersed in water.
Sec: Jr.Super60
Space for Rough Work
Page 3
Sri Chaitanya IIT Academy
25-12-2021_Jr.Super60_Jee-Main_WTM-18_Q.P
b
1)
5.
b
2
2)
b
3
3)
b
4
4)
b
5
A solid cone of uniform density and height 2R and base radius R has conical portion
scooped out its base with the same base radius but height R as shown in the figure.
The solid cone is floating in a liquid of density with vertex A touching the fluid
surface. If atmospheric pressure is P0 ,the force acting on the surface BCD due to
liquid is
A
C
R
B
6.
2R
D
1)
3P 
R3 g 
2 0 

3 
R g
2)
5R 3 g
3
3)
3P 
R3 g 
1 0 

3  R g
4)
3P 
R3 g 
5 0 

3  R g
A solid sphere of radius r and of density
is put in a liquid of density
1
2
. It got
immersed to depth h  r in the liquid then
2
1)
1
2
3)
1
2
7.
5
32
2)
25

32
4)

1

15
32

35
32
2
1
2
A sphere of radius R, made from material of specific gravity SG(>1) is submerged in a
tank of water. The sphere is placed over a hole, of radius a , in the tank bottom. For the
Sec: Jr.Super60
Space for Rough Work
Page 4
Sri Chaitanya IIT Academy
25-12-2021_Jr.Super60_Jee-Main_WTM-18_Q.P
dimensions given choose the correct options. (Neglect atmospheric pressure) and
density of water
1) Force due to liquid on the sphere is upward &
2
R3
2) Force due to liquid on the sphere is downward &
3) Force due to liquid on the sphere is upward &
8.
3
3
R3
W

g
R3
W
W
W
g
g
4) None
A uniform cylindrical block of length l density d1 and area of cross section A floats
in a liquid of density d 2 (greater than d1 ) contained in a vessel. The bottom of the
cylinder just rests on a spring of constant k. The other end of the spring is fixed to the
bottom of the vessel. A weight that may be slowly placed on top of the cylinder such
that the cylinder is just submerged in the liquid. (initially spring is at natural length )
A
l
k
Sec: Jr.Super60
Space for Rough Work
Page 5
Sri Chaitanya IIT Academy
25-12-2021_Jr.Super60_Jee-Main_WTM-18_Q.P
k

 Ag 
 d1

 k

 Ag 
 d2

1) that weight is l (d 2  d1 ) 
k
2) that weight is l (d 2  d1 ) 

 k

3) that weight is 2l d 2  d1   Ag  4) that weight is 2l d 2  d1   Ag 
 d1

 d2

9.
The mass of block is m1 and that of liquid with the vessel is m2 . The block is
suspended by a string (tension T) partially in the liquid. The reading of the weighing
machine placed below the vessel. Choose the incorrect option.
1) can be m1  m2 g
2) can be greater than m1  m2 g
3) is equal to m1 g  m2 g  T
4) can be less than m1  m2 g
10.
11.
The volume of air space in the passenger compartment of an 1800 kg car is 5.00m3 .The
volume of the motor and front wheels is 0.750m3 ,and the volume of the rear wheels, gas
tank, and trunk is 0.800m3 ,water cannot enter these two regions. The car rolls into a lake.
At first, no water enters the passanger compartment. How much of the car, in cubic
meters, is below the water surface with the car floating?
The car, with a heavy load in the trunk, remains horizontal
1) 1.8m3
2) 4.75m3
3) 2.8m3
4) 6.75m3
When researchers find a reasonably complete fossil of a dinosaur, they can determine
the mass and weight of the living dinosaur with a scale model sculpted from plastic
and based on the dimensions of the fossil bones. The scale of the model is 1/20; that
is, lengths are 1/20 of actual length, areas are (1/20)2 of actual areas, and volumes are
Sec: Jr.Super60
Space for Rough Work
Page 6
Sri Chaitanya IIT Academy
25-12-2021_Jr.Super60_Jee-Main_WTM-18_Q.P
(1/20)3 of actual volumes. First, the model is suspended from one arm of a balance
and weights are added to the other arm until equilibrium is reached. Then the model
is fully submerged in water and enough weights are removed from the second arm to
re-establish equilibrium. For a model of a particular dinosaur fossil, 637.76 g had to
be removed to reestablish equilibrium.
12.
13.
1) volume of the actual dinosaur is 637.76 cm3
2) volume of actual dinosaur is 5.102 m3
3) volume of the actual dinosaur is 637.76 m3
4) volume of actual dinosaur is 5.102 cm3
What fraction of the volume of an iceberg (density 917 kg/m3) would be visible if the
iceberg floats in the ocean (salt water, density 1024 kg/m3) (when salt water freezes to
form ice, the salt is excluded. So, an ice berg could provide fresh water to a community)
1) 0.89
2) 0.083
3) 0.1
4) 0.917
A massless conical flask filled with a liquid is kept on a table in vaccum. The force
exerted by the liquid on the base of the flask is W1 .The force exerted by the flask on
the table is W2 .
1) W1  W2
2) W1  W2  0
3) W1  W2
4) The force exerted by the liquid on the walls of the flask is W1  W2
Sec: Jr.Super60
Space for Rough Work
Page 7
Sri Chaitanya IIT Academy
14.
25-12-2021_Jr.Super60_Jee-Main_WTM-18_Q.P
Two identical communicating containers have water filled into them. A spherical ball
2
of ice (relative density = 0.9) having volume 100cm is put into left vessel.
1) If ice floats in water in the left container, then just after placing the ball the volume
of water flowing into container is 45cm3
2) If ice floats in water in the left container, then just after placing the ball the volume
of water flowing into container is 50cm3
3) If ice floats in water in the left container, then just after placing the ball the volume
of water flowing into container is 40cm 3
4) None
15.
5
1
A body floats in water with   of its volume outside the water and of its volume
9
3
16.
outside when the same body is floating in another liquid. Density of liquid in kg / m3 is
1) 1500
2) 1400
3) 1300
4) 1200
A Uniform rod of length ' l ' density is pivoted smoothly at a point ‘o' below the water
level at a depth 'h' as shown in fig. If the density of water ' ' and the rod remains
stationary. The angle made by the rod with horizontal is (h < l )
 
1) sin 1  
l 
2) sin 1
3) sin 1 l
4) sin 1 h
h
h
Sec: Jr.Super60
l
h
l
Space for Rough Work
Page 8
Sri Chaitanya IIT Academy
17.
18.
19.
An ornament weighing 36g in air, weighs only 34 g in water. Assuming that some
copper is mixed with gold to prepare the ornament, find the amount of copper in it.
Specific gravity of gold is 19.3 and that of copper is 8.9.
1) 1.2 gm
2) 2.2 gm
3) 3.2 gm
4) 4.2 gm
An open rectangular tank 5m  4m  3m high containing water upto a height of 2m is
accelerated horizontally along the longer side. The maximum acceleration that can be
given without spilling the water is ( g  10m / s 2 ).
1) 2m / s 2
2) 3m / s 2
3) 4 m / s 2
4) 5m / s 2
A closed hemispherical shell of radius R is filled with liquid which exerts a uniform
pressure p at every contact point. The net force of the liquid on the curved portion of
the shell is given by
1) 2 R 2 p
20.
25-12-2021_Jr.Super60_Jee-Main_WTM-18_Q.P
2) R 2 p
3) 4 R 2 p
4)
4 2
R p
3
An aquarium is in the shape of a cube with sides of length 60 cm. To what height
should we pour water in it so that the force on the side is one sixth of that at the
bottom? (Atmospheric pressure is not taken into account)
1) 10cm
2) 20 cm
3) 30 cm
4) 40 cm
(NUMERICAL VALUE TYPE)
This section contains 10 questions. Each question is numerical value type. For each question, enter the correct numerical
value (in decimal notation, truncated/rounded-off to second decimal place. (e.g. 6.25, 7.00, 0.33, 30, 30.27, 127.30).
Attempt any five questions out of 10.
Marking scheme: +4 for correct answer, 0 if not attempted and 0 in all other cases.
21.
Three children, each of weight 356 N, make a log raft by lashing together logs of
diameter 0.30 m and length 1.80 m. How many minimum number of logs will be
needed to keep them floating in fresh water? Take the density of the logs to be 800
kg/m3.(write the answer in integer)
Sec: Jr.Super60
Space for Rough Work
Page 9
Sri Chaitanya IIT Academy
22.
23.
24.
25.
25-12-2021_Jr.Super60_Jee-Main_WTM-18_Q.P
A sphere falls from rest into water from a height of 2m,the relative density of the
sphere is 0.8,find the depth to which ball will sink(in m).
A cubical block is floating in a liquid with half of its volume immersed in the liquid.
When the whole system accelerates upwards with acceleration of g/3,the fraction of
volume immersed in the liquid is 1/N. Then N is equal to ________
When equal volumes of two metals are mixed together, the specific gravity of alloy is
4.When equal masses of the same two metals are mixed together the specific gravity
of the alloy is 3.Calculate the ratio of specific gravity of each metal.(ratio of
higher/lower)
One end of a long iron chain of linear mass density is fixed to a sphere of mass m
and specific density 1/3 while the other end is free. The sphere along with the chain is
immersed in a deep lake. If specific density of iron is 7,the height h above the bed of
the lake at which the sphere will float in equilibrium is(Assume that part of the chain
lying on the bottom of the lake exerts negligible force on the force on the upper part
of the chain): is given as
km
where k = ?
3
h
26.
A water tank has a circular hole as its base. A solid cone is used to plug the hole
exactly half the height of the conc protrudes out of hole. Water is filled in the tank to
a height equal to height of the cone. Density of water is and volume of cone is C.
Then the hydrostatic pressure force on the cone is V g / n .Find n=?(Neglect the
atmospheric pressure)
Sec: Jr.Super60
Space for Rough Work
Page 10
Sri Chaitanya IIT Academy
27.
25-12-2021_Jr.Super60_Jee-Main_WTM-18_Q.P
A solid cone of mass m is tightly fitted inside a thin mass less spherical shell of
radius=R=6m .The apex angle of the cone is 600 and density
32
g / cm3 .The system is
9
kept immersed inside water, so that the axis of the cone lies in a horizontal plane as
shown. If it is released from this position, net torque about centre of mass of the system
3
immediately after the release is 10 12  x N  m .Find the value of x. g  10m / s 2
28.
A block of silver of mass 4 kg hanging from a string is immersed in a liquid of
relative density 0.72.If relative density of silver is 10.The tension in the string is ‘T’
N then T=.. g  10m / s 2
29.
A cube of wood of side 1m and density 500 kg/m3 is dipped in a lake of water
(density 1000 kg/m3). We want to push the cube to the bottom of the lake. The depth
of the water in lake 1m. Another person floats an identical cube in a tank of water as
shown. The cross section of the base of tank is 2m  2m and the water does not spill
out as the cube is pushed down.
30.
The force required to just hold cube at the bottom of the lake is_____kilo Newtons
A cube of ice of edge 4cm is placed in an empty cylindrical glass of inner diameter
6cm. Assume that the ice melts uniformly from side so that it always retains its
cubical shape. Remembering that ice is lighter than water, find the length of the edge
of the ice cube at the instant it just leaves contact with the bottom of the glass (in cm).
Sec: Jr.Super60
Space for Rough Work
Page 11