JEE Main 2020 Physics September 2 Shift 1 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 1
Date : 2nd September 2020
Time : 09 : 00 am - 12 : 00 pm
Subject : Physics
Q.1 The mass density of a spherical galaxy K varies as 
K
r
 over a large distance 'r' from its
centre. In that region, a small star is in a circular orbit of radius R. Then the period of
revolution, T depends on R as:
(1) 
2
T R ?
(2) 
2 3
T R ?
(3) 
2
3
1
T
R
?
(4) 
T R ?
Sol. (1)
M
R
m
Mass of galaxy = 
R
0
dv ?
?
R
2
0
k
4 r dr
r
? ?
?
R
0
4 k rdr ? ?
?
2
2
1
4 kR
M k R
2
?
? ?
F = m ?
2
R
2
2
GMm
m R
R
? ?
2
2 1
2
Gk R
R
R
? ?
2 2
k
R
? ? ?
2
k
R
? ?
2
2 R
T 2
k
?
? ? ?
?
3
T k R ?
T
2
 ? R
Page 2


JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 1
Date : 2nd September 2020
Time : 09 : 00 am - 12 : 00 pm
Subject : Physics
Q.1 The mass density of a spherical galaxy K varies as 
K
r
 over a large distance 'r' from its
centre. In that region, a small star is in a circular orbit of radius R. Then the period of
revolution, T depends on R as:
(1) 
2
T R ?
(2) 
2 3
T R ?
(3) 
2
3
1
T
R
?
(4) 
T R ?
Sol. (1)
M
R
m
Mass of galaxy = 
R
0
dv ?
?
R
2
0
k
4 r dr
r
? ?
?
R
0
4 k rdr ? ?
?
2
2
1
4 kR
M k R
2
?
? ?
F = m ?
2
R
2
2
GMm
m R
R
? ?
2
2 1
2
Gk R
R
R
? ?
2 2
k
R
? ? ?
2
k
R
? ?
2
2 R
T 2
k
?
? ? ?
?
3
T k R ?
T
2
 ? R
JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 2
Q.2 An amplitude modulated wave is represented by the expression v
m
 = 5(1 + 0.6 cos
6 2 8 0 t )
sin (211 x 10
4
 t) volts. The minimum and maximum amplitudes of the amplitude modu-
lated wave are, respectively :
(1) 
3
2
V, 5V (2) 5V, 8V (3) 3V, 5V (4) 
5
2
V, 8V
Sol. (4)
m
c
A
0.6
A
?
V
m 
=  (5+3 cos 6280t) sin (211×10
4
 t)
maximum Amp. = 5+3 = 8 V
minimum Amp. = 5–3 = 2 V
from the given option nearest value of minimum Amplitude = 
5
V
2
Q.3 A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an
object is positioned in front of the mirror, what will be the nature and magnification of
the image of the object ? (Figure drawn as schematic and not to scale)
(1) Erect, virtual and unmagnified (2) Inverted, real and magnified
(3) Erect, virtual and magnified (4) Inverted, real and unmagnified
Sol. (4)
Object
12 8 4 16
20
(cm)
C
2R
? beyond C i.e. – ? < u < C
? real, inverted
and unmagnified
Page 3


JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 1
Date : 2nd September 2020
Time : 09 : 00 am - 12 : 00 pm
Subject : Physics
Q.1 The mass density of a spherical galaxy K varies as 
K
r
 over a large distance 'r' from its
centre. In that region, a small star is in a circular orbit of radius R. Then the period of
revolution, T depends on R as:
(1) 
2
T R ?
(2) 
2 3
T R ?
(3) 
2
3
1
T
R
?
(4) 
T R ?
Sol. (1)
M
R
m
Mass of galaxy = 
R
0
dv ?
?
R
2
0
k
4 r dr
r
? ?
?
R
0
4 k rdr ? ?
?
2
2
1
4 kR
M k R
2
?
? ?
F = m ?
2
R
2
2
GMm
m R
R
? ?
2
2 1
2
Gk R
R
R
? ?
2 2
k
R
? ? ?
2
k
R
? ?
2
2 R
T 2
k
?
? ? ?
?
3
T k R ?
T
2
 ? R
JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 2
Q.2 An amplitude modulated wave is represented by the expression v
m
 = 5(1 + 0.6 cos
6 2 8 0 t )
sin (211 x 10
4
 t) volts. The minimum and maximum amplitudes of the amplitude modu-
lated wave are, respectively :
(1) 
3
2
V, 5V (2) 5V, 8V (3) 3V, 5V (4) 
5
2
V, 8V
Sol. (4)
m
c
A
0.6
A
?
V
m 
=  (5+3 cos 6280t) sin (211×10
4
 t)
maximum Amp. = 5+3 = 8 V
minimum Amp. = 5–3 = 2 V
from the given option nearest value of minimum Amplitude = 
5
V
2
Q.3 A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an
object is positioned in front of the mirror, what will be the nature and magnification of
the image of the object ? (Figure drawn as schematic and not to scale)
(1) Erect, virtual and unmagnified (2) Inverted, real and magnified
(3) Erect, virtual and magnified (4) Inverted, real and unmagnified
Sol. (4)
Object
12 8 4 16
20
(cm)
C
2R
? beyond C i.e. – ? < u < C
? real, inverted
and unmagnified
JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 3
Q.4 A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at
its sides as shown in the figure. The radius of vessel is 5 cm an and the angular speed
of rotation is ? rad s
–1
. The difference in the height, h (in cm) of liquid at the centre of
vessel and at the side will be :
(1) 
2
5
2g
?
(2) 
2
2
25g
?
(3) 
2
25
2g
?
(4) 
2
2
5g
?
Sol. (3)
h
10cm
y
2 2
x
y
2g
?
?
at x = 5cm, y=h
2 2 2
(5) 25
h
2g 2g
? ?
? ?
Page 4


JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 1
Date : 2nd September 2020
Time : 09 : 00 am - 12 : 00 pm
Subject : Physics
Q.1 The mass density of a spherical galaxy K varies as 
K
r
 over a large distance 'r' from its
centre. In that region, a small star is in a circular orbit of radius R. Then the period of
revolution, T depends on R as:
(1) 
2
T R ?
(2) 
2 3
T R ?
(3) 
2
3
1
T
R
?
(4) 
T R ?
Sol. (1)
M
R
m
Mass of galaxy = 
R
0
dv ?
?
R
2
0
k
4 r dr
r
? ?
?
R
0
4 k rdr ? ?
?
2
2
1
4 kR
M k R
2
?
? ?
F = m ?
2
R
2
2
GMm
m R
R
? ?
2
2 1
2
Gk R
R
R
? ?
2 2
k
R
? ? ?
2
k
R
? ?
2
2 R
T 2
k
?
? ? ?
?
3
T k R ?
T
2
 ? R
JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 2
Q.2 An amplitude modulated wave is represented by the expression v
m
 = 5(1 + 0.6 cos
6 2 8 0 t )
sin (211 x 10
4
 t) volts. The minimum and maximum amplitudes of the amplitude modu-
lated wave are, respectively :
(1) 
3
2
V, 5V (2) 5V, 8V (3) 3V, 5V (4) 
5
2
V, 8V
Sol. (4)
m
c
A
0.6
A
?
V
m 
=  (5+3 cos 6280t) sin (211×10
4
 t)
maximum Amp. = 5+3 = 8 V
minimum Amp. = 5–3 = 2 V
from the given option nearest value of minimum Amplitude = 
5
V
2
Q.3 A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an
object is positioned in front of the mirror, what will be the nature and magnification of
the image of the object ? (Figure drawn as schematic and not to scale)
(1) Erect, virtual and unmagnified (2) Inverted, real and magnified
(3) Erect, virtual and magnified (4) Inverted, real and unmagnified
Sol. (4)
Object
12 8 4 16
20
(cm)
C
2R
? beyond C i.e. – ? < u < C
? real, inverted
and unmagnified
JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 3
Q.4 A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at
its sides as shown in the figure. The radius of vessel is 5 cm an and the angular speed
of rotation is ? rad s
–1
. The difference in the height, h (in cm) of liquid at the centre of
vessel and at the side will be :
(1) 
2
5
2g
?
(2) 
2
2
25g
?
(3) 
2
25
2g
?
(4) 
2
2
5g
?
Sol. (3)
h
10cm
y
2 2
x
y
2g
?
?
at x = 5cm, y=h
2 2 2
(5) 25
h
2g 2g
? ?
? ?
JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 4
Q.5 If speed V, area A and force F are chosen as fundamental units, then the dimension of
Young's modulus will be
(1) FA
2
V
–3
(2) FA
2
V
–2
(3) FA
–1
V
0
(4) FA
2
V
–1
Sol. (3)
Y = k [F]
x
 [A]
y
 [V]
z
[ML
1
T
–2
] = [MLT
–2
]
x
 [L
2
]
y
 
 
[LT
–1
]
z
[ML
1
T
–2
] = [M
x
 L
x + 2y + z 
T
–2x – z
]
x = 1, –2x–z = –2, x + 2y + z = –1
? z = 0
? y = –1
Q.6 A bead of mass m stays at point P (a, b) on a wire bent in the shape of a parabola
y = 4Cx
2
 and rotating with angular speed ? (see figure). The value of ? is (neglect
friction):
(1) 
2g
C
(2) 2 gC (3) 
2gC
ab
(4) 2 2gC
Sol. (4)
y = 4 cx
2
dy
8cx
dx
?
N cos ? = mg
N sin ? = m ?
2
a
2
m a
tan
mg
?
? ?
y
0
P(a,b)
x
mg
N
tan ?=
dy
dx
=8cx
2
a
8cx
g
?
?
(x = a), 
2
a
8 c a
g
?
?
8cg ? ?
2 2gc ? ?
Page 5


JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 1
Date : 2nd September 2020
Time : 09 : 00 am - 12 : 00 pm
Subject : Physics
Q.1 The mass density of a spherical galaxy K varies as 
K
r
 over a large distance 'r' from its
centre. In that region, a small star is in a circular orbit of radius R. Then the period of
revolution, T depends on R as:
(1) 
2
T R ?
(2) 
2 3
T R ?
(3) 
2
3
1
T
R
?
(4) 
T R ?
Sol. (1)
M
R
m
Mass of galaxy = 
R
0
dv ?
?
R
2
0
k
4 r dr
r
? ?
?
R
0
4 k rdr ? ?
?
2
2
1
4 kR
M k R
2
?
? ?
F = m ?
2
R
2
2
GMm
m R
R
? ?
2
2 1
2
Gk R
R
R
? ?
2 2
k
R
? ? ?
2
k
R
? ?
2
2 R
T 2
k
?
? ? ?
?
3
T k R ?
T
2
 ? R
JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 2
Q.2 An amplitude modulated wave is represented by the expression v
m
 = 5(1 + 0.6 cos
6 2 8 0 t )
sin (211 x 10
4
 t) volts. The minimum and maximum amplitudes of the amplitude modu-
lated wave are, respectively :
(1) 
3
2
V, 5V (2) 5V, 8V (3) 3V, 5V (4) 
5
2
V, 8V
Sol. (4)
m
c
A
0.6
A
?
V
m 
=  (5+3 cos 6280t) sin (211×10
4
 t)
maximum Amp. = 5+3 = 8 V
minimum Amp. = 5–3 = 2 V
from the given option nearest value of minimum Amplitude = 
5
V
2
Q.3 A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an
object is positioned in front of the mirror, what will be the nature and magnification of
the image of the object ? (Figure drawn as schematic and not to scale)
(1) Erect, virtual and unmagnified (2) Inverted, real and magnified
(3) Erect, virtual and magnified (4) Inverted, real and unmagnified
Sol. (4)
Object
12 8 4 16
20
(cm)
C
2R
? beyond C i.e. – ? < u < C
? real, inverted
and unmagnified
JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 3
Q.4 A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at
its sides as shown in the figure. The radius of vessel is 5 cm an and the angular speed
of rotation is ? rad s
–1
. The difference in the height, h (in cm) of liquid at the centre of
vessel and at the side will be :
(1) 
2
5
2g
?
(2) 
2
2
25g
?
(3) 
2
25
2g
?
(4) 
2
2
5g
?
Sol. (3)
h
10cm
y
2 2
x
y
2g
?
?
at x = 5cm, y=h
2 2 2
(5) 25
h
2g 2g
? ?
? ?
JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 4
Q.5 If speed V, area A and force F are chosen as fundamental units, then the dimension of
Young's modulus will be
(1) FA
2
V
–3
(2) FA
2
V
–2
(3) FA
–1
V
0
(4) FA
2
V
–1
Sol. (3)
Y = k [F]
x
 [A]
y
 [V]
z
[ML
1
T
–2
] = [MLT
–2
]
x
 [L
2
]
y
 
 
[LT
–1
]
z
[ML
1
T
–2
] = [M
x
 L
x + 2y + z 
T
–2x – z
]
x = 1, –2x–z = –2, x + 2y + z = –1
? z = 0
? y = –1
Q.6 A bead of mass m stays at point P (a, b) on a wire bent in the shape of a parabola
y = 4Cx
2
 and rotating with angular speed ? (see figure). The value of ? is (neglect
friction):
(1) 
2g
C
(2) 2 gC (3) 
2gC
ab
(4) 2 2gC
Sol. (4)
y = 4 cx
2
dy
8cx
dx
?
N cos ? = mg
N sin ? = m ?
2
a
2
m a
tan
mg
?
? ?
y
0
P(a,b)
x
mg
N
tan ?=
dy
dx
=8cx
2
a
8cx
g
?
?
(x = a), 
2
a
8 c a
g
?
?
8cg ? ?
2 2gc ? ?
JEE Main 2020 Paper
         2
nd
 September 2020 | (Shift-1), Physics     Page | 5
Q.7 Magnetic materials used for making permanent magnets (P) and magnets in a trans-
former (T) have different properties of the following, which property best matches for the
type of magnet required ?
(1) P : Small retentivity, large coercivity (2) P : Large retentivity, large coercivity
(3) T : Large retentivity, large coercivity (4) T : Large retentivity, small coercivity
Sol. (2)
Permanent magnet must retain for long use and should not be easily demagnetised.
Q. 8 Interference fringes are observed on a screen by illuminating two thin slits 1 mm apart
with a light source ( ? = 632.8 nm). The distance between the screen and the slits is 100
cm. If a bright fringe is observed on screen at a distance of 1.27 mm from the central
bright fringe, then the path difference between the waves, which are reaching this point
from the slits is close to :
(1) 2.05 ?m (2) 2.87 nm (3) 2 nm (4) 1.27 ?m
Sol. (4)
given, d = 1mm
? = 632.8 nm
D = 100cm
y = 1.27 mm
y
D
x dsin
( small)
x dtan
? ? ?
? ?
? ? ?
?
3 3
2
dy 1x10 1.27 10
x
D 100 10
? ?
?
? ?
? ? ?
?
= 1.27 × 10
–6 
m
= 1.27 ?m
Q.9 A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T.
Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal
energy (in units of RT) of the mixture is:
(1) 11 (2) 13 (3) 15 (4) 20
Sol. (3)
1 2
1 v 2 v
U n C T n C T ? ?
5 3
3 RT 5x RT
2 2
? ? ?
30
RT 15RT
2
? ?