JEE Main 2020 September 3 Question Paper Shift 1 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


1. A block of mass m = 1 kg slides with velocity ? = 6 m/s on a frictionless horizontal surface and
collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings
as a result of the collision making angle ? before momentarily coming to rest. If the rod has mass
M = 2 kg, and length l = 1m, the value of ? is approximately :
(take g = 10 m/s
2
)
(1) 49° (2) 63° (3) 69° (4) 55°
Sol. 2
mv I ? ? ?
mv
I
? ?
?
2
com
1
I (m M)g (1 cos )
2
? ? ? ? ? ?
2
com
1 (mv )
(m M)g (1 cos )
2 I
? ? ? ?
?
?
2
2
M
I m
3
? ?
? ?
? ?
? ?
?
?
2 5
I 1
3 3
? ?
? ? ?
? ?
? ?
36 3 3 10 2
(1 cos )
2 5 3
? ? ?
? ? ?
?
27
(1 cos )
50
? ? ?
27
cos 1
50
? ? ?
23
cos
50
? ?
? = 63°
PHYSICS _ 3 Sep. _ SHIFT - 1
Page 2


1. A block of mass m = 1 kg slides with velocity ? = 6 m/s on a frictionless horizontal surface and
collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings
as a result of the collision making angle ? before momentarily coming to rest. If the rod has mass
M = 2 kg, and length l = 1m, the value of ? is approximately :
(take g = 10 m/s
2
)
(1) 49° (2) 63° (3) 69° (4) 55°
Sol. 2
mv I ? ? ?
mv
I
? ?
?
2
com
1
I (m M)g (1 cos )
2
? ? ? ? ? ?
2
com
1 (mv )
(m M)g (1 cos )
2 I
? ? ? ?
?
?
2
2
M
I m
3
? ?
? ?
? ?
? ?
?
?
2 5
I 1
3 3
? ?
? ? ?
? ?
? ?
36 3 3 10 2
(1 cos )
2 5 3
? ? ?
? ? ?
?
27
(1 cos )
50
? ? ?
27
cos 1
50
? ? ?
23
cos
50
? ?
? = 63°
PHYSICS _ 3 Sep. _ SHIFT - 1
2. A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block
of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is
produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it
reaches the top of the rope ?
(1) 12 (2) 3 (3) 9 (4) 6
Sol. 1
2kg
B
A
12m
m 6kg
?
?
?
6 1
kg / m
12 2
? ? ?
T
A V f ? ? ? ?
?
T '
B f ' ? ? ?
?
T
T ' '
?
?
?
20 6
' 12
80 '
? ? ? ?
?
3. When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the
diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to
be connected in series with the diode so that the current does not exceed the safe limit is :
(1) 300 ? (2) 200 ? (3) 50 ? (4) 100 ?
Sol. 4
1V
1.5v
0.5v i R
V = i R
V 1
R
i 10mA
? ?
1000
100
10
? ? ?
Page 3


1. A block of mass m = 1 kg slides with velocity ? = 6 m/s on a frictionless horizontal surface and
collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings
as a result of the collision making angle ? before momentarily coming to rest. If the rod has mass
M = 2 kg, and length l = 1m, the value of ? is approximately :
(take g = 10 m/s
2
)
(1) 49° (2) 63° (3) 69° (4) 55°
Sol. 2
mv I ? ? ?
mv
I
? ?
?
2
com
1
I (m M)g (1 cos )
2
? ? ? ? ? ?
2
com
1 (mv )
(m M)g (1 cos )
2 I
? ? ? ?
?
?
2
2
M
I m
3
? ?
? ?
? ?
? ?
?
?
2 5
I 1
3 3
? ?
? ? ?
? ?
? ?
36 3 3 10 2
(1 cos )
2 5 3
? ? ?
? ? ?
?
27
(1 cos )
50
? ? ?
27
cos 1
50
? ? ?
23
cos
50
? ?
? = 63°
PHYSICS _ 3 Sep. _ SHIFT - 1
2. A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block
of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is
produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it
reaches the top of the rope ?
(1) 12 (2) 3 (3) 9 (4) 6
Sol. 1
2kg
B
A
12m
m 6kg
?
?
?
6 1
kg / m
12 2
? ? ?
T
A V f ? ? ? ?
?
T '
B f ' ? ? ?
?
T
T ' '
?
?
?
20 6
' 12
80 '
? ? ? ?
?
3. When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the
diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to
be connected in series with the diode so that the current does not exceed the safe limit is :
(1) 300 ? (2) 200 ? (3) 50 ? (4) 100 ?
Sol. 4
1V
1.5v
0.5v i R
V = i R
V 1
R
i 10mA
? ?
1000
100
10
? ? ?
4. Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object
is measured. It should correctly be recorded as :
(1) 2.125 cm (2) 2.124 cm (3) 2.123 cm (4) 2.121 cm
Sol. 2
Least count = 
2
0.1 1
0.2 10 0.002
50 500
?
? ? ? ?
when we multiply by division no.'s
it must be even because L.C. is 0.002.
5. Model a torch battery of length ? to be made up of a thin cylindrical bar of radius ‘a’ and a
concentric thin cylindrical shell of radius ‘b’ filled in between with an electrolyte of resistivity ? (see
figure). If the battery is connected to a resistance of value R, the maximum joule heating in R will
take place for :
(1) R = 
2 l
?
?
b
a
? ?
? ?
? ?
(2) R = 
2 b
ln
l a
? ? ?
? ?
?
? ?
(3) R = 
b
ln
l a
? ? ?
? ?
?
? ?
(4) 
b
ln
2 l a
? ? ?
? ?
?
? ?
Sol. 4
dr
dR
2 r
? ?
? ?
b
a
1
dR dr
2 r
?
?
?
? ?
?
b
a
R ln(r)
2
?
? ? ?
? ?
? ?
R
cell
b
R ln
2 a
? ? ?
?
? ?
?
? ?
?
r = R
For Max heat transfer
Page 4


1. A block of mass m = 1 kg slides with velocity ? = 6 m/s on a frictionless horizontal surface and
collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings
as a result of the collision making angle ? before momentarily coming to rest. If the rod has mass
M = 2 kg, and length l = 1m, the value of ? is approximately :
(take g = 10 m/s
2
)
(1) 49° (2) 63° (3) 69° (4) 55°
Sol. 2
mv I ? ? ?
mv
I
? ?
?
2
com
1
I (m M)g (1 cos )
2
? ? ? ? ? ?
2
com
1 (mv )
(m M)g (1 cos )
2 I
? ? ? ?
?
?
2
2
M
I m
3
? ?
? ?
? ?
? ?
?
?
2 5
I 1
3 3
? ?
? ? ?
? ?
? ?
36 3 3 10 2
(1 cos )
2 5 3
? ? ?
? ? ?
?
27
(1 cos )
50
? ? ?
27
cos 1
50
? ? ?
23
cos
50
? ?
? = 63°
PHYSICS _ 3 Sep. _ SHIFT - 1
2. A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block
of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is
produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it
reaches the top of the rope ?
(1) 12 (2) 3 (3) 9 (4) 6
Sol. 1
2kg
B
A
12m
m 6kg
?
?
?
6 1
kg / m
12 2
? ? ?
T
A V f ? ? ? ?
?
T '
B f ' ? ? ?
?
T
T ' '
?
?
?
20 6
' 12
80 '
? ? ? ?
?
3. When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the
diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to
be connected in series with the diode so that the current does not exceed the safe limit is :
(1) 300 ? (2) 200 ? (3) 50 ? (4) 100 ?
Sol. 4
1V
1.5v
0.5v i R
V = i R
V 1
R
i 10mA
? ?
1000
100
10
? ? ?
4. Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object
is measured. It should correctly be recorded as :
(1) 2.125 cm (2) 2.124 cm (3) 2.123 cm (4) 2.121 cm
Sol. 2
Least count = 
2
0.1 1
0.2 10 0.002
50 500
?
? ? ? ?
when we multiply by division no.'s
it must be even because L.C. is 0.002.
5. Model a torch battery of length ? to be made up of a thin cylindrical bar of radius ‘a’ and a
concentric thin cylindrical shell of radius ‘b’ filled in between with an electrolyte of resistivity ? (see
figure). If the battery is connected to a resistance of value R, the maximum joule heating in R will
take place for :
(1) R = 
2 l
?
?
b
a
? ?
? ?
? ?
(2) R = 
2 b
ln
l a
? ? ?
? ?
?
? ?
(3) R = 
b
ln
l a
? ? ?
? ?
?
? ?
(4) 
b
ln
2 l a
? ? ?
? ?
?
? ?
Sol. 4
dr
dR
2 r
? ?
? ?
b
a
1
dR dr
2 r
?
?
?
? ?
?
b
a
R ln(r)
2
?
? ? ?
? ?
? ?
R
cell
b
R ln
2 a
? ? ?
?
? ?
?
? ?
?
r = R
For Max heat transfer
6. Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of
massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas
at temperature T is :
(1) 
3
2
 RT (2) 3RT (3) 
5
2
RT (4) 
9
2
 RT
Sol. 2
f
U nRT
2
?
6
U nRT
2
?
U = 3nRT n = 1
U = 3RT
7. An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in
magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency
?, the average power loss in the loop due to Joule heating is :
    
B
x
a
y
b
(1) 
abB
R
? ?
(2) 
2 2 2 2 2
a b B
R
? ?
(3) 
2 2 2 2 2
a b B
2R
? ?
(4) Zero
Sol. 3
BAcos t ? ? ?
d
BA sin t
dt
?
? ? ? ? ?
B ab sin t ?? ? ? ?
0
B ab ? ? ? ?
2 2 2 2 2 2
2
B a b
P (sin t)
R R
? ? ?
? ? ?
2 2 2 2 2
av
B a b
P
2R
? ?
?
Page 5


1. A block of mass m = 1 kg slides with velocity ? = 6 m/s on a frictionless horizontal surface and
collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings
as a result of the collision making angle ? before momentarily coming to rest. If the rod has mass
M = 2 kg, and length l = 1m, the value of ? is approximately :
(take g = 10 m/s
2
)
(1) 49° (2) 63° (3) 69° (4) 55°
Sol. 2
mv I ? ? ?
mv
I
? ?
?
2
com
1
I (m M)g (1 cos )
2
? ? ? ? ? ?
2
com
1 (mv )
(m M)g (1 cos )
2 I
? ? ? ?
?
?
2
2
M
I m
3
? ?
? ?
? ?
? ?
?
?
2 5
I 1
3 3
? ?
? ? ?
? ?
? ?
36 3 3 10 2
(1 cos )
2 5 3
? ? ?
? ? ?
?
27
(1 cos )
50
? ? ?
27
cos 1
50
? ? ?
23
cos
50
? ?
? = 63°
PHYSICS _ 3 Sep. _ SHIFT - 1
2. A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block
of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is
produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it
reaches the top of the rope ?
(1) 12 (2) 3 (3) 9 (4) 6
Sol. 1
2kg
B
A
12m
m 6kg
?
?
?
6 1
kg / m
12 2
? ? ?
T
A V f ? ? ? ?
?
T '
B f ' ? ? ?
?
T
T ' '
?
?
?
20 6
' 12
80 '
? ? ? ?
?
3. When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the
diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to
be connected in series with the diode so that the current does not exceed the safe limit is :
(1) 300 ? (2) 200 ? (3) 50 ? (4) 100 ?
Sol. 4
1V
1.5v
0.5v i R
V = i R
V 1
R
i 10mA
? ?
1000
100
10
? ? ?
4. Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object
is measured. It should correctly be recorded as :
(1) 2.125 cm (2) 2.124 cm (3) 2.123 cm (4) 2.121 cm
Sol. 2
Least count = 
2
0.1 1
0.2 10 0.002
50 500
?
? ? ? ?
when we multiply by division no.'s
it must be even because L.C. is 0.002.
5. Model a torch battery of length ? to be made up of a thin cylindrical bar of radius ‘a’ and a
concentric thin cylindrical shell of radius ‘b’ filled in between with an electrolyte of resistivity ? (see
figure). If the battery is connected to a resistance of value R, the maximum joule heating in R will
take place for :
(1) R = 
2 l
?
?
b
a
? ?
? ?
? ?
(2) R = 
2 b
ln
l a
? ? ?
? ?
?
? ?
(3) R = 
b
ln
l a
? ? ?
? ?
?
? ?
(4) 
b
ln
2 l a
? ? ?
? ?
?
? ?
Sol. 4
dr
dR
2 r
? ?
? ?
b
a
1
dR dr
2 r
?
?
?
? ?
?
b
a
R ln(r)
2
?
? ? ?
? ?
? ?
R
cell
b
R ln
2 a
? ? ?
?
? ?
?
? ?
?
r = R
For Max heat transfer
6. Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of
massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas
at temperature T is :
(1) 
3
2
 RT (2) 3RT (3) 
5
2
RT (4) 
9
2
 RT
Sol. 2
f
U nRT
2
?
6
U nRT
2
?
U = 3nRT n = 1
U = 3RT
7. An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in
magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency
?, the average power loss in the loop due to Joule heating is :
    
B
x
a
y
b
(1) 
abB
R
? ?
(2) 
2 2 2 2 2
a b B
R
? ?
(3) 
2 2 2 2 2
a b B
2R
? ?
(4) Zero
Sol. 3
BAcos t ? ? ?
d
BA sin t
dt
?
? ? ? ? ?
B ab sin t ?? ? ? ?
0
B ab ? ? ? ?
2 2 2 2 2 2
2
B a b
P (sin t)
R R
? ? ?
? ? ?
2 2 2 2 2
av
B a b
P
2R
? ?
?
8. A balloon filled with helium (32° C and 1.7 atm.) bursts. Immediately afterwards the expansion of
helium can be considered as :
(1) reversible isothermal (2) irreversible isothermal
(3) reversible adiabatic (4) irreversible adiabatic
Sol. 4
irreversible  adiabatic ? ?Because Energy can not be restored.
9. When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the
maximum kinetic energy of the photoelectrons becomes three times larger. The work function of
the metal is close to :
(1) 1.02 eV (2) 0.61 eV (3) 0.52 eV (4) 0.81 eV
Sol. 2
max
1
hc
KE ? ? ?
?
max
2
hc
3KE ? ? ?
?
1 2
hc hc
3
? ?
? ? ? ? ?
? ?
? ?
? ?
1 2
3hc hc
2 ? ? ?
? ?
3 1240 1240
2
500 200
?
? ? ?
0.6 ? ?
10. Two isolated conducting spheres S
1
 and S
2
 of radius 
2
3
R and 
1
3
R have 12 ?C and –3 ?C charges,
respectively, and are at a large distance from each other. They are now connected by a conduct-
ing wire. A long time after this is done the charges on S
1
 and S
2
 are respectively :
(1) 6 ?C and 3 ?C (2) 4.5 ?C on both
(3) + 4.5 ?C and –4.5 ?C (4) 3 ?C and 6 ?C
Sol. 1
12 C -3 C q
1
q
2
1 2
q q 9 C ? ? ? ..(1)