JEE Main 2020 Physics September 6 Shift 1 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 1
Date : 6th September 2020
Time : 09 : 00 am - 12 : 00 pm
Subject : Physics
1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The
square is rotating with angular frequency ?, about an axis passing through one of the
corners of the square and parallel to its diagonal, as shown in the figure. The angular
momentum of the square about this axis is :
axis
(1) 4 ml
2
? (2) 2 ml
2
? (3) 3 ml
2
? (4) ml
2
?
Sol. (3)
m
m
m
m
L = I ?
? ?
2
2
a
I m x2 m 2a
2
? ?
? ?
? ?
? ?
= ma
2
 + 2ma
2
? L = I ? ?= 3ml
2
? (a =|)
2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead
of the pitch scale marking, prior to use. Upon one complete rotation of the circular
scale, a displacement of 0.5mm is noticed on the pitch scale. The nature of zero error
involved and the least count of the screw gauge, are respectively :
(1) Positive, 0.1 mm (2) Positive, 0.1 ?m
(3) Positive, 10 ?m (4) Negative, 2 ?m
2. (3)
=
5
0.5
L.C mm 1 10 m 10 m
50
?
? ? ? ? ?
Page 2


JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 1
Date : 6th September 2020
Time : 09 : 00 am - 12 : 00 pm
Subject : Physics
1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The
square is rotating with angular frequency ?, about an axis passing through one of the
corners of the square and parallel to its diagonal, as shown in the figure. The angular
momentum of the square about this axis is :
axis
(1) 4 ml
2
? (2) 2 ml
2
? (3) 3 ml
2
? (4) ml
2
?
Sol. (3)
m
m
m
m
L = I ?
? ?
2
2
a
I m x2 m 2a
2
? ?
? ?
? ?
? ?
= ma
2
 + 2ma
2
? L = I ? ?= 3ml
2
? (a =|)
2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead
of the pitch scale marking, prior to use. Upon one complete rotation of the circular
scale, a displacement of 0.5mm is noticed on the pitch scale. The nature of zero error
involved and the least count of the screw gauge, are respectively :
(1) Positive, 0.1 mm (2) Positive, 0.1 ?m
(3) Positive, 10 ?m (4) Negative, 2 ?m
2. (3)
=
5
0.5
L.C mm 1 10 m 10 m
50
?
? ? ? ? ?
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 2
3. An electron, a doubly ionized helium ion (He
++
) and a proton are having the same kinetic
energy. The relation between their respective de-Broglie wavelengths ?
e
, 
He
? ?
? and ?
p
 is:
(1) ?
e
 > ?
P
 > 
He
? ?
? (2) ?
e
 > 
He
? ?
? > ?
P
(3) ?
e
 < ?
P
 < 
He
? ?
? (4) ?
e
 < 
He
? ?
? = ?
P
Sol. (1)
h h
p
2mK E
? ? ?
?
p
d
C
2 27
1 1
C f 55
? ? ? ? ? ? ?
m
He
 > m
P
 > m
e
?
He
 < ?
p
 < ?
e
4. For the given input voltage waveform V
in
(t), the output voltage waveform V
o
(t), across
the capacitor is correctly depicted by :
V (t)
0
0V
0
t
+5V
10 nF
(1) 
V (t)
0
2V
t
(2) 
V (t)
0
2V
t
3V
(3) 
V (t)
0
2V
t
(4) 
V (t)
0
2V
t
Sol. (2)
Answer is (2)  because capacitor is charging then discharging then again charging.
But during discharging not possible to discharge 100%.
Page 3


JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 1
Date : 6th September 2020
Time : 09 : 00 am - 12 : 00 pm
Subject : Physics
1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The
square is rotating with angular frequency ?, about an axis passing through one of the
corners of the square and parallel to its diagonal, as shown in the figure. The angular
momentum of the square about this axis is :
axis
(1) 4 ml
2
? (2) 2 ml
2
? (3) 3 ml
2
? (4) ml
2
?
Sol. (3)
m
m
m
m
L = I ?
? ?
2
2
a
I m x2 m 2a
2
? ?
? ?
? ?
? ?
= ma
2
 + 2ma
2
? L = I ? ?= 3ml
2
? (a =|)
2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead
of the pitch scale marking, prior to use. Upon one complete rotation of the circular
scale, a displacement of 0.5mm is noticed on the pitch scale. The nature of zero error
involved and the least count of the screw gauge, are respectively :
(1) Positive, 0.1 mm (2) Positive, 0.1 ?m
(3) Positive, 10 ?m (4) Negative, 2 ?m
2. (3)
=
5
0.5
L.C mm 1 10 m 10 m
50
?
? ? ? ? ?
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 2
3. An electron, a doubly ionized helium ion (He
++
) and a proton are having the same kinetic
energy. The relation between their respective de-Broglie wavelengths ?
e
, 
He
? ?
? and ?
p
 is:
(1) ?
e
 > ?
P
 > 
He
? ?
? (2) ?
e
 > 
He
? ?
? > ?
P
(3) ?
e
 < ?
P
 < 
He
? ?
? (4) ?
e
 < 
He
? ?
? = ?
P
Sol. (1)
h h
p
2mK E
? ? ?
?
p
d
C
2 27
1 1
C f 55
? ? ? ? ? ? ?
m
He
 > m
P
 > m
e
?
He
 < ?
p
 < ?
e
4. For the given input voltage waveform V
in
(t), the output voltage waveform V
o
(t), across
the capacitor is correctly depicted by :
V (t)
0
0V
0
t
+5V
10 nF
(1) 
V (t)
0
2V
t
(2) 
V (t)
0
2V
t
3V
(3) 
V (t)
0
2V
t
(4) 
V (t)
0
2V
t
Sol. (2)
Answer is (2)  because capacitor is charging then discharging then again charging.
But during discharging not possible to discharge 100%.
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 3
5. Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M,
radius of its top, R and height, H, then its moment of inertia about its axis is :
R
H
(1) 
2
2
MR
(2) 
2
3
MR
(3) 
? ?
2 2
4
M R H ?
(4) 
2
3
MH
Sol. (1)
2
mR
I
2
?
R
H
X
Y
Z
Now cut ring of thickness dx at distance x from origin.
So radius of the ring 
tan ? ? r x
, 
?
 is the half angle of cone.
dI = dm r
2
M
dm
pR L
? ?
?
? ?
? ?
 
2 p r d L
=
2MrdLcos ?
dm
RL
?
3 3
0
2M
I tan ?
RH
? ?
?
? ?
? ?
?
H
x dx
2
MR
2
Page 4


JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 1
Date : 6th September 2020
Time : 09 : 00 am - 12 : 00 pm
Subject : Physics
1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The
square is rotating with angular frequency ?, about an axis passing through one of the
corners of the square and parallel to its diagonal, as shown in the figure. The angular
momentum of the square about this axis is :
axis
(1) 4 ml
2
? (2) 2 ml
2
? (3) 3 ml
2
? (4) ml
2
?
Sol. (3)
m
m
m
m
L = I ?
? ?
2
2
a
I m x2 m 2a
2
? ?
? ?
? ?
? ?
= ma
2
 + 2ma
2
? L = I ? ?= 3ml
2
? (a =|)
2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead
of the pitch scale marking, prior to use. Upon one complete rotation of the circular
scale, a displacement of 0.5mm is noticed on the pitch scale. The nature of zero error
involved and the least count of the screw gauge, are respectively :
(1) Positive, 0.1 mm (2) Positive, 0.1 ?m
(3) Positive, 10 ?m (4) Negative, 2 ?m
2. (3)
=
5
0.5
L.C mm 1 10 m 10 m
50
?
? ? ? ? ?
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 2
3. An electron, a doubly ionized helium ion (He
++
) and a proton are having the same kinetic
energy. The relation between their respective de-Broglie wavelengths ?
e
, 
He
? ?
? and ?
p
 is:
(1) ?
e
 > ?
P
 > 
He
? ?
? (2) ?
e
 > 
He
? ?
? > ?
P
(3) ?
e
 < ?
P
 < 
He
? ?
? (4) ?
e
 < 
He
? ?
? = ?
P
Sol. (1)
h h
p
2mK E
? ? ?
?
p
d
C
2 27
1 1
C f 55
? ? ? ? ? ? ?
m
He
 > m
P
 > m
e
?
He
 < ?
p
 < ?
e
4. For the given input voltage waveform V
in
(t), the output voltage waveform V
o
(t), across
the capacitor is correctly depicted by :
V (t)
0
0V
0
t
+5V
10 nF
(1) 
V (t)
0
2V
t
(2) 
V (t)
0
2V
t
3V
(3) 
V (t)
0
2V
t
(4) 
V (t)
0
2V
t
Sol. (2)
Answer is (2)  because capacitor is charging then discharging then again charging.
But during discharging not possible to discharge 100%.
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 3
5. Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M,
radius of its top, R and height, H, then its moment of inertia about its axis is :
R
H
(1) 
2
2
MR
(2) 
2
3
MR
(3) 
? ?
2 2
4
M R H ?
(4) 
2
3
MH
Sol. (1)
2
mR
I
2
?
R
H
X
Y
Z
Now cut ring of thickness dx at distance x from origin.
So radius of the ring 
tan ? ? r x
, 
?
 is the half angle of cone.
dI = dm r
2
M
dm
pR L
? ?
?
? ?
? ?
 
2 p r d L
=
2MrdLcos ?
dm
RL
?
3 3
0
2M
I tan ?
RH
? ?
?
? ?
? ?
?
H
x dx
2
MR
2
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 4
6. A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the
satellite when it is farthest from the planet is 6 times less than that when it is closest to
the planet. The ratio of distances between the satellite and the planet at closest and
farthest points is:
(1) 1 : 2 (2) 1 : 3 (3) 1 : 6 (4) 3 : 4
Sol. (3)
O
v
6v
r
1
r
2
L
i
 = L
f
m ?6vr
1
 = m ?vr
2
6r
1
 = r
2
1
2
r 1
r 6
? ?
7. You are given that Mass of 
7
3
Li 7.0160u ? ,
Mass of 
4
2
He 4.0026u ?
and Mass of 
1
1
H 1.0079u ? .
When 20 g of 
7
3
Li is converted into 
4
2
He by proton capture, the energy liberated, (in
kWh), is: [Mass of nucleon = 1 GeV/c
2
]
(1) 6.82 × 10
5
(2) 4.5 × 10
5
(3) 8 × 10
6
(4) 1.33 × 10
6
Sol. (4)
7 4
3 1 2
Li e 2 He
?
? ?
?m ? [m
Li
 + m
H
] – 2 [M
He
]
?  ? ? m 7.0160 1.0079 2 4.0003 ? ? ? ? ?
= 0.0187
Energy released in 1 reaction ? ?mc
2
In use of 7.016 u Li energy is ?mc
2
In use of 1gm Li energy is 
Li
2
m
mc ?
In use of 20gm energy is ? 
gm 20
m
mc
Li
2
?
?
6 19 23
5
20
0.0187 931.5 10 1.6 10 6.023 10
7
36 10
?
? ? ? ? ? ? ?
?
= 1.33 × 10
6
Page 5


JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 1
Date : 6th September 2020
Time : 09 : 00 am - 12 : 00 pm
Subject : Physics
1. Four point masses, each of mass m, are fixed at the corners of a square of side l. The
square is rotating with angular frequency ?, about an axis passing through one of the
corners of the square and parallel to its diagonal, as shown in the figure. The angular
momentum of the square about this axis is :
axis
(1) 4 ml
2
? (2) 2 ml
2
? (3) 3 ml
2
? (4) ml
2
?
Sol. (3)
m
m
m
m
L = I ?
? ?
2
2
a
I m x2 m 2a
2
? ?
? ?
? ?
? ?
= ma
2
 + 2ma
2
? L = I ? ?= 3ml
2
? (a =|)
2. A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead
of the pitch scale marking, prior to use. Upon one complete rotation of the circular
scale, a displacement of 0.5mm is noticed on the pitch scale. The nature of zero error
involved and the least count of the screw gauge, are respectively :
(1) Positive, 0.1 mm (2) Positive, 0.1 ?m
(3) Positive, 10 ?m (4) Negative, 2 ?m
2. (3)
=
5
0.5
L.C mm 1 10 m 10 m
50
?
? ? ? ? ?
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 2
3. An electron, a doubly ionized helium ion (He
++
) and a proton are having the same kinetic
energy. The relation between their respective de-Broglie wavelengths ?
e
, 
He
? ?
? and ?
p
 is:
(1) ?
e
 > ?
P
 > 
He
? ?
? (2) ?
e
 > 
He
? ?
? > ?
P
(3) ?
e
 < ?
P
 < 
He
? ?
? (4) ?
e
 < 
He
? ?
? = ?
P
Sol. (1)
h h
p
2mK E
? ? ?
?
p
d
C
2 27
1 1
C f 55
? ? ? ? ? ? ?
m
He
 > m
P
 > m
e
?
He
 < ?
p
 < ?
e
4. For the given input voltage waveform V
in
(t), the output voltage waveform V
o
(t), across
the capacitor is correctly depicted by :
V (t)
0
0V
0
t
+5V
10 nF
(1) 
V (t)
0
2V
t
(2) 
V (t)
0
2V
t
3V
(3) 
V (t)
0
2V
t
(4) 
V (t)
0
2V
t
Sol. (2)
Answer is (2)  because capacitor is charging then discharging then again charging.
But during discharging not possible to discharge 100%.
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 3
5. Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M,
radius of its top, R and height, H, then its moment of inertia about its axis is :
R
H
(1) 
2
2
MR
(2) 
2
3
MR
(3) 
? ?
2 2
4
M R H ?
(4) 
2
3
MH
Sol. (1)
2
mR
I
2
?
R
H
X
Y
Z
Now cut ring of thickness dx at distance x from origin.
So radius of the ring 
tan ? ? r x
, 
?
 is the half angle of cone.
dI = dm r
2
M
dm
pR L
? ?
?
? ?
? ?
 
2 p r d L
=
2MrdLcos ?
dm
RL
?
3 3
0
2M
I tan ?
RH
? ?
?
? ?
? ?
?
H
x dx
2
MR
2
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 4
6. A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the
satellite when it is farthest from the planet is 6 times less than that when it is closest to
the planet. The ratio of distances between the satellite and the planet at closest and
farthest points is:
(1) 1 : 2 (2) 1 : 3 (3) 1 : 6 (4) 3 : 4
Sol. (3)
O
v
6v
r
1
r
2
L
i
 = L
f
m ?6vr
1
 = m ?vr
2
6r
1
 = r
2
1
2
r 1
r 6
? ?
7. You are given that Mass of 
7
3
Li 7.0160u ? ,
Mass of 
4
2
He 4.0026u ?
and Mass of 
1
1
H 1.0079u ? .
When 20 g of 
7
3
Li is converted into 
4
2
He by proton capture, the energy liberated, (in
kWh), is: [Mass of nucleon = 1 GeV/c
2
]
(1) 6.82 × 10
5
(2) 4.5 × 10
5
(3) 8 × 10
6
(4) 1.33 × 10
6
Sol. (4)
7 4
3 1 2
Li e 2 He
?
? ?
?m ? [m
Li
 + m
H
] – 2 [M
He
]
?  ? ? m 7.0160 1.0079 2 4.0003 ? ? ? ? ?
= 0.0187
Energy released in 1 reaction ? ?mc
2
In use of 7.016 u Li energy is ?mc
2
In use of 1gm Li energy is 
Li
2
m
mc ?
In use of 20gm energy is ? 
gm 20
m
mc
Li
2
?
?
6 19 23
5
20
0.0187 931.5 10 1.6 10 6.023 10
7
36 10
?
? ? ? ? ? ? ?
?
= 1.33 × 10
6
JEE Main 2020 Paper
         6
th
 September 2020 | (Shift-1), Physics     Page | 5
8. If the potential energy between two molecules is given by U = –
6 12
A B
r r
? , then at
equilibrium, separation between molecules, and the potential energy are :
(1) 
1/6
2B
A
? ?
? ?
? ?
, 
2
A
–
4B
(2) 
1/6
2B
A
? ?
? ?
? ?
, 
2
A
–
2B
(3) 
1/6
B
A
? ?
? ?
? ?
, 0 (4) 
1/6
B
2A
? ?
? ?
? ?
, 
2
A
–
2B
Sol. (1)
6 12
dU d
F ( Ar Br )
dr dr
? ?
? ?
? ? ? ?
for equation  F = 0
7 13
A( 6) B 12
0
r r
? ?
? ? ?
13 7
12B 6A
r r
?
1/6
2B
r
A
? ?
?
? ?
? ?
2
A B
U
2B
2B
A
A
?
? ?
? ?
? ?
? ?
2 2 2
A A A
2B 4B 4B
? ?
? ? ?
? Answer (1)
9. A clock has a continuously moving second’s hand of 0.1 m length. The average acceleration
of the tip of the hand (in units of ms
–2
) is of the order of:
(1) 10
–3
(2) 10
–1
(3) 10
–2
(4) 10
–4
Sol. (1)
2
v
a
R
?
2 R
v
60
?
?
? ?
2 2 2
3
2 2 2
4 R 4 R 4
10 0.1 10
(60) (60)
60 R
?
? ? ?
? ? ? ? ? ?