AITS-OT-II (Paper-2)-PCM-JEE(Advanced)/21 2
Physics PART – I
SECTION – A
(One or More than one correct type)
This section contains 08 questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR
MORE THAN ONE of these four options is(are) correct.
1. A soap bubble of radius ‘r’ and wall thickness ‘h’ is made in vacuum by blowing an ideal diatomic
gas in it. The surface tension of the soap solution is ‘’ and density of the soap solution is ‘’.
Assume that the heat capacity of the soap film is much greater than that of the gas in the bubble.
Then choose the correct option(s). (R = ideal gas constant)
(A) The molar heat capacity of the gas in the bubble is 4R.
(B) The molar heat capacity of the gas in the bubble is 3R.
hr2
(C) The time period of small radial oscillations of the soap film is 2
8
hr2
(D) The time period of small radial oscillations of the soap film is 2
4
2. Two uncharged thin concentric spherical conducting shells ‘A’ and ‘B’ of 3R
radii R and 3R are connected through a resistance ‘r’ and switch ‘S’
initially opened as shown in the figure. A positive point charge ‘Q’ is
fixed at a distance 2R from the centre of the shells. At t = 0, the switch +Q 2R s r
‘S’ is closed till the steady state is reached. Then choose the correct O
R
option(s).
(A) The total heat dissipated in the resistor ‘r’ is Q2
96 0R
(B) The total heat dissipated in the resistor ‘r’ is Q2
192 0 R
Q
(C) The charge on the outer surface of shell ‘A’ after steady state reached is .
4
(D) The charge on the outer surface of shell ‘B’ after steady state reached is +Q.
3. A uniform circular ring of mass ‘m’ and radius ‘R’ is hinged at O
its top point ‘O’ and suspended in a vertical plane so that it m, R
can freely rotate about a horizontal axis passing through the
hinge ‘O’ as shown in the figure. The bead ‘A’ is rigidly
attached to the ring and the bead ‘B’ can slide without friction A
on the ring. The mass of each bead is ‘m’. The system is B
released from rest from the initial position shown in the figure.
Then choose the correct option(s), immediately after the
system is released from rest. (Take g = 10 m/s2)
(A) The acceleration of bead ‘A’ is 2 2 m/s2.
(B) The acceleration of bead ‘A’ is 2 m/s2.
(C) The acceleration of bead ‘B’ is 2 m/s2.
(D) The acceleration of bead ‘B’ is 2 26 m/s2.
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3 AITS-OT-II (Paper-2)-PCM-JEE(Advanced)/21
4. A thin uniform rod AB of mass m = 1kg and length = 1m is hinged at end
‘A’. The rod makes an angle = 53 with the vertical axis and it is rotating A
with a constant angular velocity ‘’ about the vertical axis passing through m,
end ‘A’ as shown in the figure. Then choose the correct option(s).
(A) The angular velocity ‘’ must be 5 rad/s.
(B) The angular velocity ‘’ must be 10 rad/s.
(C) The net hinge reaction on the rod at end ‘A’ is 10 2 N.
(D) The net hinge reaction on the rod at end ‘A’ is 10 N.
5. Consider an arrangement of a thin biprism and screen as shown in the figure. The refraction
angle of the biprism is A = 4 and the refractive index of its material is = 1.5. The wavelength of
the monochromatic light emitted by the source ‘S’ is = 6000 Å. Then choose the correct
option(s).
screen
A
S
a = 25cm b = 100cm
(A) The fringe width of the interference pattern obtained on the screen is 21.5 m.
(B) The fringe width of the interference pattern obtained on the screen is 43 m.
(C) If the source ‘S’ is located at large distance from the biprism then the fringe width
obtained on the screen will be 8.6 m.
(D) If the source ‘S’ is located at large distance from the biprism then the fringe width
obtained on the screen will be 17.2 m.
6. A conducting rod of mass ‘m’ and length ‘’ is placed
B
on a pair of smooth horizontal conducting parallel B F = 2mg
rails connected at one end by an inductor of L C
inductance L and by a capacitor of capacitance ‘C’ at
the other end as shown in the figure. A uniform m,
vertical magnetic field ‘B’ exists in the region
perpendicular to the plane of rails. The conductor
starts from rest at t = 0 from the left end of the rails
due to constant external horizontal force F = 2mg
applied to it. Then choose the correct option(s). (Take
CB22 = m)
8mgL
(A) The maximum horizontal displacement of the rod is
B22
4mgL
(B) The maximum horizontal displacement of the rod is
B22
B
(C) The angular frequency of the oscillations of the rod is
mL
B
(D) The angular frequency of the oscillations of the rod is
2m L
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7. A square loop of side ‘a’ and carrying current ‘I’
is placed at a distance d = a from an infinitely
long straight wire carrying the same current ‘I’ as I
a
shown in the figure. The perpendicular bisector I
I
plane of the square loop contains the long a
straight current carrying wire. Then choose the
correct options(s). I
d=a
I
a
a
I
(A) The magnitude of force acting on the square loop due to long current carrying wire is
2 0 I2
5
(B) The magnitude of force acting on the square loop due to long current carrying wire is
0I2
5
2 0 I2 a
(C) The torque experienced by the square loop due to long current carrying wire is
5
0 I2 a
(D) The torque experienced by the square loop due to long current carrying wire is
5
8. In the circuit as shown in the adjoining C1 = 6F C2 = 3F
figure the switch S1 is closed at t = 0. After
steady state is reached, the switch S2 is
also closed for a long time. Then choose S2
the correct option(s).
1 = 100V 2 = 50V
3 = 80V
S1
(A) The heat dissipated in the circuit after the switch ‘S2’ is closed will be 100 J.
(B) The heat dissipated in the circuit after the switch ‘S2’ is closed will be 50 J.
(C) The charge flown through the battery 1 after closing the switch ‘S2’ is 20 C.
(D) The charge flown through the battery 2 after closing the switch ‘S2’ is 10 C.
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5 AITS-OT-II (Paper-2)-PCM-JEE(Advanced)/21
(Matching List Type)
This section contains TWO (02) List-Match Sets. Each List-Match set has TWO(02) Multiple Choice
Questions. Each List-Match set has two lists: List-I and List-II. List-I has Four entries (I), (II), (III) and
(IV) and List-II has Six entries (P), (Q), (R), (S), (T) and (U). FOUR options are given in each Multiple
Choice Question based On List-I and List-II and ONLY ONE of these four options satisfies the condition
asked in the Multiple Choice Question.
Answer the following by appropriately matching the list based on the information given in the
paragraph.
Two long current carrying thin walled coaxial cylinders are depicted in List-I and List-II gives the
magnitude of magnetic pressure exerted on the wall of the cylinders.
List– I List- II
2a
I I 0I2
(I) a
(P)
32 2 a 2
2a
2I 0I2
(II) 2I (Q)
a 82a2
2a
I/2 3 0I2
(III) 2I (R)
a 16 2 a 2
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AITS-OT-II (Paper-2)-PCM-JEE(Advanced)/21 6
2a
3I/2 3I
9 0I2
(IV) a
(S)
32 2 a 2
0I2
(T)
22a2
9 0I2
(U)
16 2 a 2
9. Find the correct match for the magnetic pressure exerted on the wall of each inner cylinder.
(A) (I) (Q), (II) (T), (III) (P), (IV) (S)
(B) (I) (P), (II) (T), (III) (S), (IV) (R)
(C) (I) (Q), (II) (T), (III) (R), (IV) (S)
(D) (I) (P), (II) (S), (III) (R), (IV) (Q)
10. Find the correct match for the magnetic pressure exerted on the wall of each outer cylinder.
(A) (I) (P), (II) (Q), (III) (T), (IV) (S)
(B) (I) (Q), (II) (S), (III) (R), (IV) (U)
(C) (I) (P), (II) (Q), (III) (R), (IV) (U)
(D) (I) (S), (II) (T), (III) (R), (IV) (P)
Answer the following by appropriately matching the list based on the information given in the
paragraph.
One mole of an ideal gas is taken through four different cyclic processes as depicted in the List-I
and List-II gives the values of total work done and total heat absorbed by the gas during four
different cyclic processes.
List– I List- II
P
2P0 B
P0V0
(I) P0 A (P)
C 2
V0 2V0 V
monoatomic gas is taken
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7 AITS-OT-II (Paper-2)-PCM-JEE(Advanced)/21
P
A B
P0
P0/4 C
(II) (Q) P0 V0
V0 2V0 4V0 V
monoatomic gas is taken
(For the process BC, PV2 = constant and
process CA is an isothermal process)
P
A
4P0
B
P0
(III) P0/2 (R) 2 P0 V0 (1 n2)
C
V0 2V0 V
Diatomic gas is taken
(For the process AB, PV2 = constant and for
the process CA, PV3 = constant)
P
A B
P0
P0/2 C
5P0 V0
(IV) P0/4 D (S)
2
V0 2V0 4V0 V
Diatomic gas is taken
(Processes BC and DA are isothermal)
(T) 6 P0 V0
P0 V0
(U) (7 4n2)
2
11. Find the correct match for the total work done by the gas during each cyclic process.
(A) (I) (S), (II) (R), (III) (P), (IV) (T)
(B) (I) (P), (II) (R), (III) (P), (IV) (Q)
(C) (I) (P), (II) (Q), (III) (R), (IV) (T)
(D) (I) (Q), (II) (P), (III) (S), (IV) (R)
12. Find the correct match for the total heat absorbed by the gas during each cyclic process.
(A) (I) (Q), (II) (S), (III) (T), (IV) (P)
(B) (I) (T), (II) (S), (III) (Q), (IV) (R)
(C) (I) (T), (II) (S), (III) (T), (IV) (U)
(D) (I) (P), (II) (S), (III) (R), (IV) (Q)
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SECTION – C
(Numerical Answer Type)
This section contains 06 questions. The answer to each question is a NUMERICAL VALUE. For each
question, enter the correct numerical value (in decimal notation, truncated/rounded‐off to the second
decimal place; e.g. XXXXX.XX).
13. Three small balls A, B and C of masses m, 2m and 2m
respectively are placed on a smooth horizontal surface. Balls m 2m
A and B as well as B and C are connected by light A B
inextensible strings each of equal length . The string
connecting balls A and B is taut. The initial distance between
3
3
the balls B and C is and BC is perpendicular to AB. 2
2
The ball ‘C’ is given a horizontal velocity v 0 = 20.7 m/s 2m C
parallel to AB as shown in the figure. Find the initial velocity v0
(in m/s) of the ball ‘A’.
14. A cylinder and a wedge with a vertical face touching each
other, move along two smooth inclined planes making the
same angle = 45 with the horizontal as shown in the m2
m1
figure. The masses of the cylinder and the wedge are m 1 =
5 kg and m2 = 3 kg respectively. There is no friction
between the cylinder and the wedge. Find the normal force = 45 = 45
(in Newton) acting between the cylinder and the wedge.
(Take g = 10 m/s2)
15. A satellite is projected into space from a point ‘P’ at a distance ‘r0’ v0
GM P
from the centre of the earth with an initial velocity v0 at an
r0
angle = 37 with the horizontal at point ‘P’ as shown in the figure. r0
It is found that the satellite is propelled into an elliptical orbit. Find
the eccentricity of the elliptical orbit.
O M
16. Two wires of same length = 1 m and same cross-sectional 1,Y1,,A 2,Y2,,A
area A = 10 mm2 are welded together and their ends are A B
rigidly clamped between two walls as shown in the figure. 1 O 2
Given
1 = 2 105 C1, Y1 = 1 1010 N/m2, 1 = 0.4 kg/m
2 = 1 105 C1, Y2 = 2 1010 N/m2, 2 = 0.1 kg/m
The tension in the wires is produced by reducing the temperature of system by 20C. Find the
first overtone frequency (in Hz) of transverse vibration of the system with joint ‘O’ as a node.
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17. A metallic surface is illuminated alternatively with electromagnetic radiations of wavelengths
4500A0 and 6000A0. It is observed that the maximum speeds of the photoelectrons emitted
under these illuminations are in the ratio 2 :1. Find the work function (in eV) of the metal. (Take
hC = 1242 eV-nm)
18. The pitch of a screw gauge is 1 mm and its circular scale is divided into 100 divisions. When
nothing is placed between its studs, the zero of the circular scale lies 6 divisions below the
reference line. When a wire is placed between its studs, the main scale reading is 2 mm and 56th
division of circular scale coincides with the reference line of the main scale. The length of wire is
8.68 cm. Find the curved surface area (in cm 2) of the wire in true significant figures.
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