JEE Main 2020 Physics September 6 Shift 2 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 1
Date : 6th September 2020
Time : 02 : 00 pm - 05 : 00 pm
Subject : Physics
Q.1 For a plane electromagnetic wave, the magnetic field at a point x and time t is
? ? ? ?
7 3 11
ˆ
B x,t 1.2 10 sin 0.5 10 x 1.5 10 t k T
?
? ?
? ? ? ? ?
? ?
?
The instantaneous electric field 
E
?
 corresponding to 
B
?
 is :
(speed of light c = 3 × 10
8
 ms
–1
)
(1) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 1 10 x 1.5 10 t i
m
? ?
? ? ? ?
? ?
?
(2) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 0.5 10 x 1.5 10 t k
m
? ?
? ? ? ?
? ?
?
(3) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 1 10 x 0.5 10 t j
m
? ?
? ? ? ?
? ?
?
(4) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 0.5 10 x 1.5 10 t j
m
? ?
? ? ? ? ?
? ?
?
Sol. 4
|E| |B |C ?
? ?
x
?
? ? ? ?
7 3
1.2 10 sin| 0.5 10
 + 1.5×10
11
t ) × 3 ×10
8
? 36 sin (0.5×10
3
x+1.5×10
11
t)
? ?  Not change ?  Answer 1, 3 incorrect
E
?
 and 
B
?
 ? not same direction ? 2nd incorrect
Q.2 Particle A of mass m
1
 moving with velocity ? ?
1
ˆ ˆ
3i j ms
?
?
 collides with another particle B
of mass m
2
 which is at rest initially. Let 
1
V
?
 and 
2
V
?
 be the velocities of particles A and B
after collision respectively. If m
1
 = 2m
2
 and after collision ? ?
–1
1
ˆ ˆ
V i 3j ms ? ?
?
, the angle
between 
1
V
?
 and 
2
V
?
 is :
(1) 105° (2) 15° (3) –45° (4) 60°
Sol. 1
From momentum conservation
(2m) 
ˆ ˆ
( 3 i j) ? +0 = 2m 
2
ˆ ˆ
(i 3j) mv ? ?
?
? ? 2
ˆ ˆ
V 2( 3 1) (i j) ? ? ?
? ? ?
and ? ?
? ? ?
1
ˆ ˆ
V i 3 j
60°
45°
V
1
V
2
so angle b/w 
? ? ?
1
v and 
2
V
? ? ?
 is 105°.
Page 2


JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 1
Date : 6th September 2020
Time : 02 : 00 pm - 05 : 00 pm
Subject : Physics
Q.1 For a plane electromagnetic wave, the magnetic field at a point x and time t is
? ? ? ?
7 3 11
ˆ
B x,t 1.2 10 sin 0.5 10 x 1.5 10 t k T
?
? ?
? ? ? ? ?
? ?
?
The instantaneous electric field 
E
?
 corresponding to 
B
?
 is :
(speed of light c = 3 × 10
8
 ms
–1
)
(1) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 1 10 x 1.5 10 t i
m
? ?
? ? ? ?
? ?
?
(2) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 0.5 10 x 1.5 10 t k
m
? ?
? ? ? ?
? ?
?
(3) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 1 10 x 0.5 10 t j
m
? ?
? ? ? ?
? ?
?
(4) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 0.5 10 x 1.5 10 t j
m
? ?
? ? ? ? ?
? ?
?
Sol. 4
|E| |B |C ?
? ?
x
?
? ? ? ?
7 3
1.2 10 sin| 0.5 10
 + 1.5×10
11
t ) × 3 ×10
8
? 36 sin (0.5×10
3
x+1.5×10
11
t)
? ?  Not change ?  Answer 1, 3 incorrect
E
?
 and 
B
?
 ? not same direction ? 2nd incorrect
Q.2 Particle A of mass m
1
 moving with velocity ? ?
1
ˆ ˆ
3i j ms
?
?
 collides with another particle B
of mass m
2
 which is at rest initially. Let 
1
V
?
 and 
2
V
?
 be the velocities of particles A and B
after collision respectively. If m
1
 = 2m
2
 and after collision ? ?
–1
1
ˆ ˆ
V i 3j ms ? ?
?
, the angle
between 
1
V
?
 and 
2
V
?
 is :
(1) 105° (2) 15° (3) –45° (4) 60°
Sol. 1
From momentum conservation
(2m) 
ˆ ˆ
( 3 i j) ? +0 = 2m 
2
ˆ ˆ
(i 3j) mv ? ?
?
? ? 2
ˆ ˆ
V 2( 3 1) (i j) ? ? ?
? ? ?
and ? ?
? ? ?
1
ˆ ˆ
V i 3 j
60°
45°
V
1
V
2
so angle b/w 
? ? ?
1
v and 
2
V
? ? ?
 is 105°.
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 2
Q.3 When a car is at rest, its driver sees rain drops falling on it vertically. When driving the
car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal.
On further increasing the speed of the car to (1 + ?)v, this angle changes to 45°. The
value of ? is close to:
(1) 0.50 (2) 0.73 (3) 0.37 (4) 0.41
Sol. 2
rm r m
V V V ? ?
? ? ? ? ? ? ? ? ? ? ?
60°
V
V
r
45°
V
r
(I case)
st
(II case)
nd
r
v
tan60
v
? ...(1)
r
v
tan45
(1 )v
?
? ?
...(2)
from (1)/(2)
3 1 / 4
1 1 / (1 )v
?
? ?
3 1 0.732 ? ? ? ? ? ?
Q.4 A charged particle going around in a circle can be considered to be a current loop. A
particle of mass m carrying charge q is moving in a plane with speed v under the
influence of magnetic field 
B
?
. The magnetic moment of this moving particle:
(1) 
2
2
mv B
2B
?
(2) 
2
2
mv B
2 B
?
?
?
(3) 
2
2
mv B
2B
?
?
(4) 
2
2
mv B
B
?
?
Sol. 3
Magnetic dipole moment
M = iA
? i = qF, A = ?R
2
qB
F ,
2 m
?
?
mv
R
qB
?
2 2
2 2
qB m v
M q
2 m q B
? ? ? ?
? ? ?
? ? ? ?
?
? ? ? ?
?
2
mV
M
2B
B
V
qVB
dir
n
 of 
M
?
 and B
?
 is opposite.
? ?
? ?
?
2
mV
ˆ
M . B
2B
?
?
?
2
2
mV
B
2B
Page 3


JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 1
Date : 6th September 2020
Time : 02 : 00 pm - 05 : 00 pm
Subject : Physics
Q.1 For a plane electromagnetic wave, the magnetic field at a point x and time t is
? ? ? ?
7 3 11
ˆ
B x,t 1.2 10 sin 0.5 10 x 1.5 10 t k T
?
? ?
? ? ? ? ?
? ?
?
The instantaneous electric field 
E
?
 corresponding to 
B
?
 is :
(speed of light c = 3 × 10
8
 ms
–1
)
(1) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 1 10 x 1.5 10 t i
m
? ?
? ? ? ?
? ?
?
(2) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 0.5 10 x 1.5 10 t k
m
? ?
? ? ? ?
? ?
?
(3) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 1 10 x 0.5 10 t j
m
? ?
? ? ? ?
? ?
?
(4) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 0.5 10 x 1.5 10 t j
m
? ?
? ? ? ? ?
? ?
?
Sol. 4
|E| |B |C ?
? ?
x
?
? ? ? ?
7 3
1.2 10 sin| 0.5 10
 + 1.5×10
11
t ) × 3 ×10
8
? 36 sin (0.5×10
3
x+1.5×10
11
t)
? ?  Not change ?  Answer 1, 3 incorrect
E
?
 and 
B
?
 ? not same direction ? 2nd incorrect
Q.2 Particle A of mass m
1
 moving with velocity ? ?
1
ˆ ˆ
3i j ms
?
?
 collides with another particle B
of mass m
2
 which is at rest initially. Let 
1
V
?
 and 
2
V
?
 be the velocities of particles A and B
after collision respectively. If m
1
 = 2m
2
 and after collision ? ?
–1
1
ˆ ˆ
V i 3j ms ? ?
?
, the angle
between 
1
V
?
 and 
2
V
?
 is :
(1) 105° (2) 15° (3) –45° (4) 60°
Sol. 1
From momentum conservation
(2m) 
ˆ ˆ
( 3 i j) ? +0 = 2m 
2
ˆ ˆ
(i 3j) mv ? ?
?
? ? 2
ˆ ˆ
V 2( 3 1) (i j) ? ? ?
? ? ?
and ? ?
? ? ?
1
ˆ ˆ
V i 3 j
60°
45°
V
1
V
2
so angle b/w 
? ? ?
1
v and 
2
V
? ? ?
 is 105°.
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 2
Q.3 When a car is at rest, its driver sees rain drops falling on it vertically. When driving the
car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal.
On further increasing the speed of the car to (1 + ?)v, this angle changes to 45°. The
value of ? is close to:
(1) 0.50 (2) 0.73 (3) 0.37 (4) 0.41
Sol. 2
rm r m
V V V ? ?
? ? ? ? ? ? ? ? ? ? ?
60°
V
V
r
45°
V
r
(I case)
st
(II case)
nd
r
v
tan60
v
? ...(1)
r
v
tan45
(1 )v
?
? ?
...(2)
from (1)/(2)
3 1 / 4
1 1 / (1 )v
?
? ?
3 1 0.732 ? ? ? ? ? ?
Q.4 A charged particle going around in a circle can be considered to be a current loop. A
particle of mass m carrying charge q is moving in a plane with speed v under the
influence of magnetic field 
B
?
. The magnetic moment of this moving particle:
(1) 
2
2
mv B
2B
?
(2) 
2
2
mv B
2 B
?
?
?
(3) 
2
2
mv B
2B
?
?
(4) 
2
2
mv B
B
?
?
Sol. 3
Magnetic dipole moment
M = iA
? i = qF, A = ?R
2
qB
F ,
2 m
?
?
mv
R
qB
?
2 2
2 2
qB m v
M q
2 m q B
? ? ? ?
? ? ?
? ? ? ?
?
? ? ? ?
?
2
mV
M
2B
B
V
qVB
dir
n
 of 
M
?
 and B
?
 is opposite.
? ?
? ?
?
2
mV
ˆ
M . B
2B
?
?
?
2
2
mV
B
2B
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 3
Q.5 A double convex lens has power P and same radii of curvature R of both the surfaces.
The radius of curvature of a surface of a plano-convex lens made of the same material
with power 1.5 P is:
(1) 
R
3
(2) 
3R
2
(3) 
R
2
(4) 2R
Sol. 1
? ? ? ? ?
? ?
? ?
? ?
?
? ?
? ?
?
s
2
P 1
R
...(1)
? ? ? ? ?
? ?
? ? ? ?
?
? ? ? ?
?
S 1
3 1
P 1
2 R
...(2)
from (1)/(2)
?
1
P 2 / R
3 1 / R
P
2
R
1
 = R/3
Q.6 A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected
correctly to the resistor. In the circuit:
(1) Ammeter is always connected in series and voltmeter in parallel
(2) Both, ammeter and voltmeter must be connected in series
(3) Both ammeter and voltmeter must be connected in parallel
(4) ammeter is always used in parallel and voltmeter is series
Sol. 1
A
V
By theory
In order for a voltmeter to measure a device's voltage, it must be connected in parallel
to that device. This is necessary because objects in parallel experience the same potential
difference.
A voltmeter measures the potential difference of the circuit and it has high internal
resistance. When the voltmeter is connected in parallel with a circuit component, the
amount of current passing through the voltmeter is very less. Therefore, the current
through the circuit is unaltered.
In order for an ammeter to measure a device's current, it must be connected in series to
that device. This is necessary because objects in series experience the same current.
Q.7 A square loop of side 2a and carrying current I is kept in xz plane with its centre at
origin. A long wire carrying the same current I is placed parallel to z-axis and passing
through point (0, b, 0), (b >> a). The magnitude of torque on the loop about z-axis will
be:
(1) 
2 2
0
2 I a
b
?
?
(2) 
? ?
2 2
0
2 2
2 I a b
a b
?
? ?
(3) 
2 2
0
I a
2 b
?
?
(4) 
? ?
2 2
0
2 2
I a b
2 a b
?
? ?
Page 4


JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 1
Date : 6th September 2020
Time : 02 : 00 pm - 05 : 00 pm
Subject : Physics
Q.1 For a plane electromagnetic wave, the magnetic field at a point x and time t is
? ? ? ?
7 3 11
ˆ
B x,t 1.2 10 sin 0.5 10 x 1.5 10 t k T
?
? ?
? ? ? ? ?
? ?
?
The instantaneous electric field 
E
?
 corresponding to 
B
?
 is :
(speed of light c = 3 × 10
8
 ms
–1
)
(1) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 1 10 x 1.5 10 t i
m
? ?
? ? ? ?
? ?
?
(2) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 0.5 10 x 1.5 10 t k
m
? ?
? ? ? ?
? ?
?
(3) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 1 10 x 0.5 10 t j
m
? ?
? ? ? ?
? ?
?
(4) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 0.5 10 x 1.5 10 t j
m
? ?
? ? ? ? ?
? ?
?
Sol. 4
|E| |B |C ?
? ?
x
?
? ? ? ?
7 3
1.2 10 sin| 0.5 10
 + 1.5×10
11
t ) × 3 ×10
8
? 36 sin (0.5×10
3
x+1.5×10
11
t)
? ?  Not change ?  Answer 1, 3 incorrect
E
?
 and 
B
?
 ? not same direction ? 2nd incorrect
Q.2 Particle A of mass m
1
 moving with velocity ? ?
1
ˆ ˆ
3i j ms
?
?
 collides with another particle B
of mass m
2
 which is at rest initially. Let 
1
V
?
 and 
2
V
?
 be the velocities of particles A and B
after collision respectively. If m
1
 = 2m
2
 and after collision ? ?
–1
1
ˆ ˆ
V i 3j ms ? ?
?
, the angle
between 
1
V
?
 and 
2
V
?
 is :
(1) 105° (2) 15° (3) –45° (4) 60°
Sol. 1
From momentum conservation
(2m) 
ˆ ˆ
( 3 i j) ? +0 = 2m 
2
ˆ ˆ
(i 3j) mv ? ?
?
? ? 2
ˆ ˆ
V 2( 3 1) (i j) ? ? ?
? ? ?
and ? ?
? ? ?
1
ˆ ˆ
V i 3 j
60°
45°
V
1
V
2
so angle b/w 
? ? ?
1
v and 
2
V
? ? ?
 is 105°.
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 2
Q.3 When a car is at rest, its driver sees rain drops falling on it vertically. When driving the
car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal.
On further increasing the speed of the car to (1 + ?)v, this angle changes to 45°. The
value of ? is close to:
(1) 0.50 (2) 0.73 (3) 0.37 (4) 0.41
Sol. 2
rm r m
V V V ? ?
? ? ? ? ? ? ? ? ? ? ?
60°
V
V
r
45°
V
r
(I case)
st
(II case)
nd
r
v
tan60
v
? ...(1)
r
v
tan45
(1 )v
?
? ?
...(2)
from (1)/(2)
3 1 / 4
1 1 / (1 )v
?
? ?
3 1 0.732 ? ? ? ? ? ?
Q.4 A charged particle going around in a circle can be considered to be a current loop. A
particle of mass m carrying charge q is moving in a plane with speed v under the
influence of magnetic field 
B
?
. The magnetic moment of this moving particle:
(1) 
2
2
mv B
2B
?
(2) 
2
2
mv B
2 B
?
?
?
(3) 
2
2
mv B
2B
?
?
(4) 
2
2
mv B
B
?
?
Sol. 3
Magnetic dipole moment
M = iA
? i = qF, A = ?R
2
qB
F ,
2 m
?
?
mv
R
qB
?
2 2
2 2
qB m v
M q
2 m q B
? ? ? ?
? ? ?
? ? ? ?
?
? ? ? ?
?
2
mV
M
2B
B
V
qVB
dir
n
 of 
M
?
 and B
?
 is opposite.
? ?
? ?
?
2
mV
ˆ
M . B
2B
?
?
?
2
2
mV
B
2B
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 3
Q.5 A double convex lens has power P and same radii of curvature R of both the surfaces.
The radius of curvature of a surface of a plano-convex lens made of the same material
with power 1.5 P is:
(1) 
R
3
(2) 
3R
2
(3) 
R
2
(4) 2R
Sol. 1
? ? ? ? ?
? ?
? ?
? ?
?
? ?
? ?
?
s
2
P 1
R
...(1)
? ? ? ? ?
? ?
? ? ? ?
?
? ? ? ?
?
S 1
3 1
P 1
2 R
...(2)
from (1)/(2)
?
1
P 2 / R
3 1 / R
P
2
R
1
 = R/3
Q.6 A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected
correctly to the resistor. In the circuit:
(1) Ammeter is always connected in series and voltmeter in parallel
(2) Both, ammeter and voltmeter must be connected in series
(3) Both ammeter and voltmeter must be connected in parallel
(4) ammeter is always used in parallel and voltmeter is series
Sol. 1
A
V
By theory
In order for a voltmeter to measure a device's voltage, it must be connected in parallel
to that device. This is necessary because objects in parallel experience the same potential
difference.
A voltmeter measures the potential difference of the circuit and it has high internal
resistance. When the voltmeter is connected in parallel with a circuit component, the
amount of current passing through the voltmeter is very less. Therefore, the current
through the circuit is unaltered.
In order for an ammeter to measure a device's current, it must be connected in series to
that device. This is necessary because objects in series experience the same current.
Q.7 A square loop of side 2a and carrying current I is kept in xz plane with its centre at
origin. A long wire carrying the same current I is placed parallel to z-axis and passing
through point (0, b, 0), (b >> a). The magnitude of torque on the loop about z-axis will
be:
(1) 
2 2
0
2 I a
b
?
?
(2) 
? ?
2 2
0
2 2
2 I a b
a b
?
? ?
(3) 
2 2
0
I a
2 b
?
?
(4) 
? ?
2 2
0
2 2
I a b
2 a b
?
? ?
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 4
Sol. 2
other view
B
AD
F=i.2aB
b
2a
B
F=i.2aB
BC
?
x
i
0
2 2
i
B
2 a b
?
?
? ?
? torque = F cos ? . 2 a
= 
0
2 2
i.2a. i
2 a b
?
? ?
 
?
2 2
b
.2a
a b
= 
?
? ?
2 2
0
2 2
2 i a b
(a b )
Q.8 In a dilute gas at pressure P and temperature T, the mean time between successive
collisions of a molecule varies with T as:
(1) 
T
(2) 
1
T
(3) T (4) 
1
T
Sol. 4
V
avg.
 ? 
T
T
mean
 = 
avg
V
?
T
mean
 ? 
1
T
Page 5


JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 1
Date : 6th September 2020
Time : 02 : 00 pm - 05 : 00 pm
Subject : Physics
Q.1 For a plane electromagnetic wave, the magnetic field at a point x and time t is
? ? ? ?
7 3 11
ˆ
B x,t 1.2 10 sin 0.5 10 x 1.5 10 t k T
?
? ?
? ? ? ? ?
? ?
?
The instantaneous electric field 
E
?
 corresponding to 
B
?
 is :
(speed of light c = 3 × 10
8
 ms
–1
)
(1) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 1 10 x 1.5 10 t i
m
? ?
? ? ? ?
? ?
?
(2) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 0.5 10 x 1.5 10 t k
m
? ?
? ? ? ?
? ?
?
(3) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 1 10 x 0.5 10 t j
m
? ?
? ? ? ?
? ?
?
(4) ? ? ? ?
3 11
V
ˆ
E x,t 36sin 0.5 10 x 1.5 10 t j
m
? ?
? ? ? ? ?
? ?
?
Sol. 4
|E| |B |C ?
? ?
x
?
? ? ? ?
7 3
1.2 10 sin| 0.5 10
 + 1.5×10
11
t ) × 3 ×10
8
? 36 sin (0.5×10
3
x+1.5×10
11
t)
? ?  Not change ?  Answer 1, 3 incorrect
E
?
 and 
B
?
 ? not same direction ? 2nd incorrect
Q.2 Particle A of mass m
1
 moving with velocity ? ?
1
ˆ ˆ
3i j ms
?
?
 collides with another particle B
of mass m
2
 which is at rest initially. Let 
1
V
?
 and 
2
V
?
 be the velocities of particles A and B
after collision respectively. If m
1
 = 2m
2
 and after collision ? ?
–1
1
ˆ ˆ
V i 3j ms ? ?
?
, the angle
between 
1
V
?
 and 
2
V
?
 is :
(1) 105° (2) 15° (3) –45° (4) 60°
Sol. 1
From momentum conservation
(2m) 
ˆ ˆ
( 3 i j) ? +0 = 2m 
2
ˆ ˆ
(i 3j) mv ? ?
?
? ? 2
ˆ ˆ
V 2( 3 1) (i j) ? ? ?
? ? ?
and ? ?
? ? ?
1
ˆ ˆ
V i 3 j
60°
45°
V
1
V
2
so angle b/w 
? ? ?
1
v and 
2
V
? ? ?
 is 105°.
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 2
Q.3 When a car is at rest, its driver sees rain drops falling on it vertically. When driving the
car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal.
On further increasing the speed of the car to (1 + ?)v, this angle changes to 45°. The
value of ? is close to:
(1) 0.50 (2) 0.73 (3) 0.37 (4) 0.41
Sol. 2
rm r m
V V V ? ?
? ? ? ? ? ? ? ? ? ? ?
60°
V
V
r
45°
V
r
(I case)
st
(II case)
nd
r
v
tan60
v
? ...(1)
r
v
tan45
(1 )v
?
? ?
...(2)
from (1)/(2)
3 1 / 4
1 1 / (1 )v
?
? ?
3 1 0.732 ? ? ? ? ? ?
Q.4 A charged particle going around in a circle can be considered to be a current loop. A
particle of mass m carrying charge q is moving in a plane with speed v under the
influence of magnetic field 
B
?
. The magnetic moment of this moving particle:
(1) 
2
2
mv B
2B
?
(2) 
2
2
mv B
2 B
?
?
?
(3) 
2
2
mv B
2B
?
?
(4) 
2
2
mv B
B
?
?
Sol. 3
Magnetic dipole moment
M = iA
? i = qF, A = ?R
2
qB
F ,
2 m
?
?
mv
R
qB
?
2 2
2 2
qB m v
M q
2 m q B
? ? ? ?
? ? ?
? ? ? ?
?
? ? ? ?
?
2
mV
M
2B
B
V
qVB
dir
n
 of 
M
?
 and B
?
 is opposite.
? ?
? ?
?
2
mV
ˆ
M . B
2B
?
?
?
2
2
mV
B
2B
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 3
Q.5 A double convex lens has power P and same radii of curvature R of both the surfaces.
The radius of curvature of a surface of a plano-convex lens made of the same material
with power 1.5 P is:
(1) 
R
3
(2) 
3R
2
(3) 
R
2
(4) 2R
Sol. 1
? ? ? ? ?
? ?
? ?
? ?
?
? ?
? ?
?
s
2
P 1
R
...(1)
? ? ? ? ?
? ?
? ? ? ?
?
? ? ? ?
?
S 1
3 1
P 1
2 R
...(2)
from (1)/(2)
?
1
P 2 / R
3 1 / R
P
2
R
1
 = R/3
Q.6 A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected
correctly to the resistor. In the circuit:
(1) Ammeter is always connected in series and voltmeter in parallel
(2) Both, ammeter and voltmeter must be connected in series
(3) Both ammeter and voltmeter must be connected in parallel
(4) ammeter is always used in parallel and voltmeter is series
Sol. 1
A
V
By theory
In order for a voltmeter to measure a device's voltage, it must be connected in parallel
to that device. This is necessary because objects in parallel experience the same potential
difference.
A voltmeter measures the potential difference of the circuit and it has high internal
resistance. When the voltmeter is connected in parallel with a circuit component, the
amount of current passing through the voltmeter is very less. Therefore, the current
through the circuit is unaltered.
In order for an ammeter to measure a device's current, it must be connected in series to
that device. This is necessary because objects in series experience the same current.
Q.7 A square loop of side 2a and carrying current I is kept in xz plane with its centre at
origin. A long wire carrying the same current I is placed parallel to z-axis and passing
through point (0, b, 0), (b >> a). The magnitude of torque on the loop about z-axis will
be:
(1) 
2 2
0
2 I a
b
?
?
(2) 
? ?
2 2
0
2 2
2 I a b
a b
?
? ?
(3) 
2 2
0
I a
2 b
?
?
(4) 
? ?
2 2
0
2 2
I a b
2 a b
?
? ?
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 4
Sol. 2
other view
B
AD
F=i.2aB
b
2a
B
F=i.2aB
BC
?
x
i
0
2 2
i
B
2 a b
?
?
? ?
? torque = F cos ? . 2 a
= 
0
2 2
i.2a. i
2 a b
?
? ?
 
?
2 2
b
.2a
a b
= 
?
? ?
2 2
0
2 2
2 i a b
(a b )
Q.8 In a dilute gas at pressure P and temperature T, the mean time between successive
collisions of a molecule varies with T as:
(1) 
T
(2) 
1
T
(3) T (4) 
1
T
Sol. 4
V
avg.
 ? 
T
T
mean
 = 
avg
V
?
T
mean
 ? 
1
T
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-2), Physics     Page | 5
Q.9 When a particle of mass m is attached to a vertical spring of spring constant k and
released, its motion is described by y(t) = y
0
sin
2
?t, where 'y' is measured from the lower
end of unstretched spring. Then ? is:
(1) 
0
g
y
(2) 
0
1 g
2 y
(3) 
0
2g
y
(4) 
0
g
2y
9. 4
M.P.
0
y
y(t)
2
? (1 – cos(2 ?t))
From comparing standard equation of SHM Amplitude A = 
0
y
2
At equilibrium situation 
0
y mg
k 2
?
0
2g k
y m
?
k
2
m
? ?
1 k
2 m
? ?
0
1 2g
2 y
? ?
? ?
0
1 g
y
2
Q.10 The linear mass density of a thin rod AB of length L varies from A to B as 
? ?
0
x
x 1
L
? ?
? ? ? ?
? ?
? ?
,
where x is the distance from A. If M is the mass of the rod then its moment of inertia
about an axis passing through A and perpendicular to the rod is:
(1) 
2
2
ML
5
(2) 
2
5
ML
12
(3) 
2
7
ML
18
(4) 
2
3
ML
7
Sol. 3
x ? ?
? ? ?
? ?
? ?
0
dm 1 dx
L