JEE Main 2020 September 3 Question Paper Shift 2 | JEE Main & Advanced Previous Year Papers PDF Download

 Page 1


1. A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on
a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through
its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of
f is :
(1) 
1
2
(2) 
1
2
(3) 1 (4) 2
Sol. 4
1 max
V V A ? ? ?
m
m
m
m
A
A'
2 max
V V A ' ' ? ? ?
A ? = A’ ?’
k 2k
A A'
m m
?
A’ = 
2
A
2. The mass density of a planet of radius R varies with the distance r from its centre as ?(r) = ?
0
2
2
r
1
R
? ?
?
? ?
? ?
. Then the gravitational field is maximum at :
(1) r = 
1
3
R (2) r = 
3
4
R (3) r = R (4) r = 
5
9
R
Sol. 4
dr
r
dm dv ? ?
2
2
0 2
r
dm 1 4 r dr
R
? ?
? ? ? ?
? ?
? ?
? ?
PHYSICS _ 3 Sep. _ SHIFT - 2
Page 2


1. A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on
a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through
its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of
f is :
(1) 
1
2
(2) 
1
2
(3) 1 (4) 2
Sol. 4
1 max
V V A ? ? ?
m
m
m
m
A
A'
2 max
V V A ' ' ? ? ?
A ? = A’ ?’
k 2k
A A'
m m
?
A’ = 
2
A
2. The mass density of a planet of radius R varies with the distance r from its centre as ?(r) = ?
0
2
2
r
1
R
? ?
?
? ?
? ?
. Then the gravitational field is maximum at :
(1) r = 
1
3
R (2) r = 
3
4
R (3) r = R (4) r = 
5
9
R
Sol. 4
dr
r
dm dv ? ?
2
2
0 2
r
dm 1 4 r dr
R
? ?
? ? ? ?
? ?
? ?
? ?
PHYSICS _ 3 Sep. _ SHIFT - 2
3 5
0 2
r r
M 4
3 5R
? ?
? ? ? ?
? ?
? ?
g 2
GM
E
r
?
3
g 0 2
r r
E G4
3 5R
? ?
? ? ? ?
? ?
? ?
2
g
2
dE
1 3r
0
dr 3 5R
? ? ?
2
2
1 3 r
3 5 R
?
5
r R
9
?
3. Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respec-
tively. Both the sources emit light of the same power 200 W. The ratio of the number density of
photons of X-rays to the number density of photons of the visible light of the given wavelengths is :
(1) 
1
500
(2) 
1
250
(3) 500 (4) 250
Sol. 1
nhc
P ?
?
n
const ?
?
1 1
2 2
n 1nm 1
n 500nm 500
?
? ? ?
?
4. If a semiconductor photodiode can detect a photon with a maximum wavelength of 400 nm, then
its band gap energy is :
Planck’s constant h = 6.63 × 10
–34
 J.s. Speed of light c = 3 × 10
8
 m/s
(1) 1.5 eV (2) 2.0 eV (3) 3.1 eV (4) 1.1 eV
Sol. 3
hc
E ?
?
Page 3


1. A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on
a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through
its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of
f is :
(1) 
1
2
(2) 
1
2
(3) 1 (4) 2
Sol. 4
1 max
V V A ? ? ?
m
m
m
m
A
A'
2 max
V V A ' ' ? ? ?
A ? = A’ ?’
k 2k
A A'
m m
?
A’ = 
2
A
2. The mass density of a planet of radius R varies with the distance r from its centre as ?(r) = ?
0
2
2
r
1
R
? ?
?
? ?
? ?
. Then the gravitational field is maximum at :
(1) r = 
1
3
R (2) r = 
3
4
R (3) r = R (4) r = 
5
9
R
Sol. 4
dr
r
dm dv ? ?
2
2
0 2
r
dm 1 4 r dr
R
? ?
? ? ? ?
? ?
? ?
? ?
PHYSICS _ 3 Sep. _ SHIFT - 2
3 5
0 2
r r
M 4
3 5R
? ?
? ? ? ?
? ?
? ?
g 2
GM
E
r
?
3
g 0 2
r r
E G4
3 5R
? ?
? ? ? ?
? ?
? ?
2
g
2
dE
1 3r
0
dr 3 5R
? ? ?
2
2
1 3 r
3 5 R
?
5
r R
9
?
3. Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respec-
tively. Both the sources emit light of the same power 200 W. The ratio of the number density of
photons of X-rays to the number density of photons of the visible light of the given wavelengths is :
(1) 
1
500
(2) 
1
250
(3) 500 (4) 250
Sol. 1
nhc
P ?
?
n
const ?
?
1 1
2 2
n 1nm 1
n 500nm 500
?
? ? ?
?
4. If a semiconductor photodiode can detect a photon with a maximum wavelength of 400 nm, then
its band gap energy is :
Planck’s constant h = 6.63 × 10
–34
 J.s. Speed of light c = 3 × 10
8
 m/s
(1) 1.5 eV (2) 2.0 eV (3) 3.1 eV (4) 1.1 eV
Sol. 3
hc
E ?
?
34 8
9
6.63 10 3 10
E
400 10
?
?
? ? ?
?
?
1240
E eV
400
?
E = 3.1 eV
5. Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar
constant. Dimension of solar constant is :
(1) ML
0
T
–3
(2) MLT
–2
(3) M
2
L
0
T
–1
(4) ML
2
T
–2
Sol. 1
Q
E
At
?
2 2
2
ML T
E
L T
?
?
E = MT
-3
6. A particle is moving unidirectionally on a horizontal plane under the action of a constant power
supplying energy source. The displacement (s) - time (t) graph that describes the motion of the
particle is (graphs are drawn schematically and are not to scale) :
(1) (2) 
(3) (4) 
Sol. 2
P = FV
dv
P m v
dt
?
P
vdv dt
m
?
2
V k 't ?
V k '' t ?
3/2
s  t ?
Page 4


1. A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on
a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through
its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of
f is :
(1) 
1
2
(2) 
1
2
(3) 1 (4) 2
Sol. 4
1 max
V V A ? ? ?
m
m
m
m
A
A'
2 max
V V A ' ' ? ? ?
A ? = A’ ?’
k 2k
A A'
m m
?
A’ = 
2
A
2. The mass density of a planet of radius R varies with the distance r from its centre as ?(r) = ?
0
2
2
r
1
R
? ?
?
? ?
? ?
. Then the gravitational field is maximum at :
(1) r = 
1
3
R (2) r = 
3
4
R (3) r = R (4) r = 
5
9
R
Sol. 4
dr
r
dm dv ? ?
2
2
0 2
r
dm 1 4 r dr
R
? ?
? ? ? ?
? ?
? ?
? ?
PHYSICS _ 3 Sep. _ SHIFT - 2
3 5
0 2
r r
M 4
3 5R
? ?
? ? ? ?
? ?
? ?
g 2
GM
E
r
?
3
g 0 2
r r
E G4
3 5R
? ?
? ? ? ?
? ?
? ?
2
g
2
dE
1 3r
0
dr 3 5R
? ? ?
2
2
1 3 r
3 5 R
?
5
r R
9
?
3. Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respec-
tively. Both the sources emit light of the same power 200 W. The ratio of the number density of
photons of X-rays to the number density of photons of the visible light of the given wavelengths is :
(1) 
1
500
(2) 
1
250
(3) 500 (4) 250
Sol. 1
nhc
P ?
?
n
const ?
?
1 1
2 2
n 1nm 1
n 500nm 500
?
? ? ?
?
4. If a semiconductor photodiode can detect a photon with a maximum wavelength of 400 nm, then
its band gap energy is :
Planck’s constant h = 6.63 × 10
–34
 J.s. Speed of light c = 3 × 10
8
 m/s
(1) 1.5 eV (2) 2.0 eV (3) 3.1 eV (4) 1.1 eV
Sol. 3
hc
E ?
?
34 8
9
6.63 10 3 10
E
400 10
?
?
? ? ?
?
?
1240
E eV
400
?
E = 3.1 eV
5. Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar
constant. Dimension of solar constant is :
(1) ML
0
T
–3
(2) MLT
–2
(3) M
2
L
0
T
–1
(4) ML
2
T
–2
Sol. 1
Q
E
At
?
2 2
2
ML T
E
L T
?
?
E = MT
-3
6. A particle is moving unidirectionally on a horizontal plane under the action of a constant power
supplying energy source. The displacement (s) - time (t) graph that describes the motion of the
particle is (graphs are drawn schematically and are not to scale) :
(1) (2) 
(3) (4) 
Sol. 2
P = FV
dv
P m v
dt
?
P
vdv dt
m
?
2
V k 't ?
V k '' t ?
3/2
s  t ?
7. Which of the following will NOT be observed when a multimeter (operating in resistance measuring
mode) probes connected across a component, are just reversed ?
(1) Multimeter shows NO deflection in both cases i.e. before and after reversing the probes if the
chosen component is metal wire.
(2) Multimeter shows a deflection, accompanied by a splash of light out of connected component in
one direction and NO deflection on reversing the probes if the chosen component is LED.
(3) Multimeter shows an equal deflection in both cases i.e. before and after reversing the probes if
the chosen component is resistor.
(4) Multimeter shows NO deflection in both cases i.e. before and after reversing the probes if the
chosen component is capacitor.
Sol. 4
By Theory
8. A uniform rod of length ‘l’ is pivoted at one of its ends on a vertical shaft of negligible radius.
When the shaft rotates at angular speed ? the rod makes an angle ? with it (see figure). To find ?
equate the rate of change of angular momentum (direction going into the paper) 
2
ml
12
?
2 
sin ? cos ?
about the centre of mass (CM) to the torque provided by the horizontal and vertical forces F
H
 and
F
V
 about the CM. The value of ? is then such that :
(1) cos ? = 
2
2g
3l ?
(2) cos ? =
2
3g
2l ?
(3) cos ? =
2
g
2l ?
(4) cos ? = 
2
g
l ?
Sol. 2
F
V
F
H
Mg
Page 5


1. A block of mass m attached to a massless spring is performing oscillatory motion of amplitude ‘A’ on
a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through
its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of
f is :
(1) 
1
2
(2) 
1
2
(3) 1 (4) 2
Sol. 4
1 max
V V A ? ? ?
m
m
m
m
A
A'
2 max
V V A ' ' ? ? ?
A ? = A’ ?’
k 2k
A A'
m m
?
A’ = 
2
A
2. The mass density of a planet of radius R varies with the distance r from its centre as ?(r) = ?
0
2
2
r
1
R
? ?
?
? ?
? ?
. Then the gravitational field is maximum at :
(1) r = 
1
3
R (2) r = 
3
4
R (3) r = R (4) r = 
5
9
R
Sol. 4
dr
r
dm dv ? ?
2
2
0 2
r
dm 1 4 r dr
R
? ?
? ? ? ?
? ?
? ?
? ?
PHYSICS _ 3 Sep. _ SHIFT - 2
3 5
0 2
r r
M 4
3 5R
? ?
? ? ? ?
? ?
? ?
g 2
GM
E
r
?
3
g 0 2
r r
E G4
3 5R
? ?
? ? ? ?
? ?
? ?
2
g
2
dE
1 3r
0
dr 3 5R
? ? ?
2
2
1 3 r
3 5 R
?
5
r R
9
?
3. Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respec-
tively. Both the sources emit light of the same power 200 W. The ratio of the number density of
photons of X-rays to the number density of photons of the visible light of the given wavelengths is :
(1) 
1
500
(2) 
1
250
(3) 500 (4) 250
Sol. 1
nhc
P ?
?
n
const ?
?
1 1
2 2
n 1nm 1
n 500nm 500
?
? ? ?
?
4. If a semiconductor photodiode can detect a photon with a maximum wavelength of 400 nm, then
its band gap energy is :
Planck’s constant h = 6.63 × 10
–34
 J.s. Speed of light c = 3 × 10
8
 m/s
(1) 1.5 eV (2) 2.0 eV (3) 3.1 eV (4) 1.1 eV
Sol. 3
hc
E ?
?
34 8
9
6.63 10 3 10
E
400 10
?
?
? ? ?
?
?
1240
E eV
400
?
E = 3.1 eV
5. Amount of solar energy received on the earth’s surface per unit area per unit time is defined a solar
constant. Dimension of solar constant is :
(1) ML
0
T
–3
(2) MLT
–2
(3) M
2
L
0
T
–1
(4) ML
2
T
–2
Sol. 1
Q
E
At
?
2 2
2
ML T
E
L T
?
?
E = MT
-3
6. A particle is moving unidirectionally on a horizontal plane under the action of a constant power
supplying energy source. The displacement (s) - time (t) graph that describes the motion of the
particle is (graphs are drawn schematically and are not to scale) :
(1) (2) 
(3) (4) 
Sol. 2
P = FV
dv
P m v
dt
?
P
vdv dt
m
?
2
V k 't ?
V k '' t ?
3/2
s  t ?
7. Which of the following will NOT be observed when a multimeter (operating in resistance measuring
mode) probes connected across a component, are just reversed ?
(1) Multimeter shows NO deflection in both cases i.e. before and after reversing the probes if the
chosen component is metal wire.
(2) Multimeter shows a deflection, accompanied by a splash of light out of connected component in
one direction and NO deflection on reversing the probes if the chosen component is LED.
(3) Multimeter shows an equal deflection in both cases i.e. before and after reversing the probes if
the chosen component is resistor.
(4) Multimeter shows NO deflection in both cases i.e. before and after reversing the probes if the
chosen component is capacitor.
Sol. 4
By Theory
8. A uniform rod of length ‘l’ is pivoted at one of its ends on a vertical shaft of negligible radius.
When the shaft rotates at angular speed ? the rod makes an angle ? with it (see figure). To find ?
equate the rate of change of angular momentum (direction going into the paper) 
2
ml
12
?
2 
sin ? cos ?
about the centre of mass (CM) to the torque provided by the horizontal and vertical forces F
H
 and
F
V
 about the CM. The value of ? is then such that :
(1) cos ? = 
2
2g
3l ?
(2) cos ? =
2
3g
2l ?
(3) cos ? =
2
g
2l ?
(4) cos ? = 
2
g
l ?
Sol. 2
F
V
F
H
Mg
F
V
 = mg
F
H
 = 
2
m sin
2
? ?
?
?
net
? about COM = 
V H
F . sin F cos
2 2
? ? ?
? ?
= 
2
2
m
sin cos
12
? ? ?
?
2
2 2
m
mg sin m sin cos sin cos
2 2 2 12
? ? ? ? ? ? ? ? ?
? ? ? ?
2 2 2
2
g
cos cos
2 4 12
?
? ? ? ? ? ?
? ? ?
2 2
g 1 1
cos
2 12 4
? ?
? ? ? ?
? ?
? ?
?
?
2 2
g cos
2 3
? ?
?
? ?
2
g
cos
2
?
? ?
? ?
9. Two resistors 400 ? and 800 ? are connected in series across a 6 V battery. The potential differ-
ence measured by a voltmeter of 10 k ? across 400 ? resistor is close to :
(1) 2.05 V (2) 2 V (3) 1.95 V (4) 1.8 V
Sol. 3
6
i
400 10000
800
400 10000
?
?
?
?
6
i
40000
800
104
?
?
6 6
i 0.00506
800 384.61 1184.61
? ? ?
?
v
V 6 800 0.00506 6 4.05 1.95 ? ? ? ? ? ?