JEE Main 2021 Physics March 17 Shift 1 Paper & Solutions | Mock Tests for JEE Main and Advanced 2025 PDF Download

 Page 1


 
 
17
th
 March. 2021 | Shift 1 
SECTION – A 
1. The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a 
measurement it was noted that 'o' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier  
coincidence is 6, then the correct value of measurement is ……………………. cm.  
 (least count = 0.01 cm) 
 (1) 8.36 cm  (2) 8.56 cm  (3) 8.58 cm  (4) 8.54 cm 
Sol. (4) 
 Reading = MSR + VSD × LC – zero error 
 Reading = 8.5 + 
(0.1) 6 0.2
10 10
?
? =8.54 cm 
 
2. For what value of displacement the kinetic energy and potential energy of a simple harmonic 
oscillation become equal ?  
 (1) x = 
A
2
 (2) x = 0  (3) x = ? A  (4) x = ? 
A
2
 
Sol. (4) 
 KE = PE 
 
2 2 2
1 1
k(A – X ) KX
2 2
? 
 
2 2 2
A – X X ? 
 
2 2
2X A ? 
 
2
2
A
X
2
? 
 
A
X
2
? ? 
 
3. An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to 
that of photon is : (c being  the velocity of light)  
 (1) 
1/2
E
2m
? ?
? ?
?
?
?
? ?
? ?
  (2) 
1
c
 
1/2
E
2m
? ?
? ?
?
?
?
? ?
? ?
  (3) c(2mE)
1/2
  (4) 
1
c
1/2
2m
E
? ?
? ?
?
?
?
? ?
? ?
 
Sol. (2) 
 For photon E = 
hc
?
 
  
P
hc
E
? ? …(i) 
 For electron   
e
hc
2mE
? ? …(ii) 
 
1/2
e
2
p
hc
E 1 E
2mE
hc c 2m
2mc
E
? ? ?
? ?
? ? ? ?
?
?
? ?
? ? ?
 
Page 2


 
 
17
th
 March. 2021 | Shift 1 
SECTION – A 
1. The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a 
measurement it was noted that 'o' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier  
coincidence is 6, then the correct value of measurement is ……………………. cm.  
 (least count = 0.01 cm) 
 (1) 8.36 cm  (2) 8.56 cm  (3) 8.58 cm  (4) 8.54 cm 
Sol. (4) 
 Reading = MSR + VSD × LC – zero error 
 Reading = 8.5 + 
(0.1) 6 0.2
10 10
?
? =8.54 cm 
 
2. For what value of displacement the kinetic energy and potential energy of a simple harmonic 
oscillation become equal ?  
 (1) x = 
A
2
 (2) x = 0  (3) x = ? A  (4) x = ? 
A
2
 
Sol. (4) 
 KE = PE 
 
2 2 2
1 1
k(A – X ) KX
2 2
? 
 
2 2 2
A – X X ? 
 
2 2
2X A ? 
 
2
2
A
X
2
? 
 
A
X
2
? ? 
 
3. An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to 
that of photon is : (c being  the velocity of light)  
 (1) 
1/2
E
2m
? ?
? ?
?
?
?
? ?
? ?
  (2) 
1
c
 
1/2
E
2m
? ?
? ?
?
?
?
? ?
? ?
  (3) c(2mE)
1/2
  (4) 
1
c
1/2
2m
E
? ?
? ?
?
?
?
? ?
? ?
 
Sol. (2) 
 For photon E = 
hc
?
 
  
P
hc
E
? ? …(i) 
 For electron   
e
hc
2mE
? ? …(ii) 
 
1/2
e
2
p
hc
E 1 E
2mE
hc c 2m
2mc
E
? ? ?
? ?
? ? ? ?
?
?
? ?
? ? ?
 
 
 
4. A car accelerates from rest at a constant rate ? for some time after which it decelerates at a 
constant  rate ? to  come to rest. If the total time elapsed is t seconds, the total distance 
travelled is : ?
 (1) 
2( )
? ?
? ? ?
t
2
  (2) 
4( )
? ?
? ? ?
t
2
  (3) 
4
( )
? ?
? ? ?
t
2
  (4) 
2
( )
? ?
? ? ?
t
2
 
Sol. (1) 
 
  
 
 t
1
 + t
2
 = t, V' = 0 + ?t
1
 
 V = u + at 
 0 = ?t
1
 – ?t
2
 
 
2 1
t t
?
?
?
 
 
1 1
t t t
?
? ?
?
 
 
1
t t
? ? ?
?
? ?
? ? ?
? ?
 
  
Distance  = 
1 2 1
1
(t t ) t
2
? ? ? area of triangle 
 
1
t t
2 a
? ? ?
? ? ?
? ?
? ?
? ?
 
 
2
t
2( )
? ?
?
? ? ?
 
 
5. A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The 
amount of heat energy supplied to the engine from the source in each cycle is : 
 (1) 1800 J  (2) 3200 J  (3) 2400 J  (4) 1600 J  
Sol. (3) 
 
1
1
2
? ? ? 
 
1
2
? ? 
 ? ?
W
Q
 
 
1200 1
Q 2
? 
 Q = 2400 J 
V 
?t
1
t
1 t
2
t
Page 3


 
 
17
th
 March. 2021 | Shift 1 
SECTION – A 
1. The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a 
measurement it was noted that 'o' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier  
coincidence is 6, then the correct value of measurement is ……………………. cm.  
 (least count = 0.01 cm) 
 (1) 8.36 cm  (2) 8.56 cm  (3) 8.58 cm  (4) 8.54 cm 
Sol. (4) 
 Reading = MSR + VSD × LC – zero error 
 Reading = 8.5 + 
(0.1) 6 0.2
10 10
?
? =8.54 cm 
 
2. For what value of displacement the kinetic energy and potential energy of a simple harmonic 
oscillation become equal ?  
 (1) x = 
A
2
 (2) x = 0  (3) x = ? A  (4) x = ? 
A
2
 
Sol. (4) 
 KE = PE 
 
2 2 2
1 1
k(A – X ) KX
2 2
? 
 
2 2 2
A – X X ? 
 
2 2
2X A ? 
 
2
2
A
X
2
? 
 
A
X
2
? ? 
 
3. An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to 
that of photon is : (c being  the velocity of light)  
 (1) 
1/2
E
2m
? ?
? ?
?
?
?
? ?
? ?
  (2) 
1
c
 
1/2
E
2m
? ?
? ?
?
?
?
? ?
? ?
  (3) c(2mE)
1/2
  (4) 
1
c
1/2
2m
E
? ?
? ?
?
?
?
? ?
? ?
 
Sol. (2) 
 For photon E = 
hc
?
 
  
P
hc
E
? ? …(i) 
 For electron   
e
hc
2mE
? ? …(ii) 
 
1/2
e
2
p
hc
E 1 E
2mE
hc c 2m
2mc
E
? ? ?
? ?
? ? ? ?
?
?
? ?
? ? ?
 
 
 
4. A car accelerates from rest at a constant rate ? for some time after which it decelerates at a 
constant  rate ? to  come to rest. If the total time elapsed is t seconds, the total distance 
travelled is : ?
 (1) 
2( )
? ?
? ? ?
t
2
  (2) 
4( )
? ?
? ? ?
t
2
  (3) 
4
( )
? ?
? ? ?
t
2
  (4) 
2
( )
? ?
? ? ?
t
2
 
Sol. (1) 
 
  
 
 t
1
 + t
2
 = t, V' = 0 + ?t
1
 
 V = u + at 
 0 = ?t
1
 – ?t
2
 
 
2 1
t t
?
?
?
 
 
1 1
t t t
?
? ?
?
 
 
1
t t
? ? ?
?
? ?
? ? ?
? ?
 
  
Distance  = 
1 2 1
1
(t t ) t
2
? ? ? area of triangle 
 
1
t t
2 a
? ? ?
? ? ?
? ?
? ?
? ?
 
 
2
t
2( )
? ?
?
? ? ?
 
 
5. A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The 
amount of heat energy supplied to the engine from the source in each cycle is : 
 (1) 1800 J  (2) 3200 J  (3) 2400 J  (4) 1600 J  
Sol. (3) 
 
1
1
2
? ? ? 
 
1
2
? ? 
 ? ?
W
Q
 
 
1200 1
Q 2
? 
 Q = 2400 J 
V 
?t
1
t
1 t
2
t
 
 
17
th
 March. 2021 | Shift 1 
6. A mass M hangs  on a massless rod of length l which rotates at a constant angular frequency. 
The mass M moves with steady speed in a circular path of constant radius. Assume that the 
system is in steady circular motion with constant angular velocity ?. The angular momentum of 
M about point A is L
A
 which lies in the positive z direction and the angular momentum of M 
about point B is L
B
. The correct statement for this system is : 
 
 
M A
r
?
?
B
z
? ?
  
 (1) L
A
 and L
B
 are both constant in magnitude and direction 
 (2) L
B
 is constant, both in magnitude and direction  
 (3) L
A
 is contant, both in magnitude and direction 
  (4) L
B
 is constant  in direction with varying magnitude  
Sol. (3) 
 
x
?
v
?
L
?
r
   
 ? ?
A
L r p
?
? ?
 
 as r p ? so L
A
 = constant 
 
7. Two ideal polyatomic  gases at temperatures T
1
 and T
2
 are mixed so that there is no loss of 
energy. If F
1
 and F
2
 , m
1
 and m
2
, n
1
 and n
2
 be the degress of freedom, masses, number of  
molecules of the first and second gas respectively, the temperature of mixture  of these two 
gases is : 
 (1) 
1 1 1 2 2 2
1 1 2 2
n F T n F T
n F n F
?
?
  (2) 
1 1 1 2 2 2
1 2
n F T n F T
F F
?
?
  (3) 
1 1 1 2 2 2
1 2
n F T n F T
n n
?
?
  (4) 
1 1 2 2
1 2
n T n T
n n
?
?
  
Sol. (1) 
 initial internal energy  = final internal energy 
 
1 2 1 2
1 1 2 2 1 2
F F F F
n RT n RT n RT n RT
2 2 2 2
? ? ? 
 
1 1 1 2 2 2
1 1 2 2
F n T F n T
T
Fn F n
?
?
?
 
Page 4


 
 
17
th
 March. 2021 | Shift 1 
SECTION – A 
1. The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a 
measurement it was noted that 'o' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier  
coincidence is 6, then the correct value of measurement is ……………………. cm.  
 (least count = 0.01 cm) 
 (1) 8.36 cm  (2) 8.56 cm  (3) 8.58 cm  (4) 8.54 cm 
Sol. (4) 
 Reading = MSR + VSD × LC – zero error 
 Reading = 8.5 + 
(0.1) 6 0.2
10 10
?
? =8.54 cm 
 
2. For what value of displacement the kinetic energy and potential energy of a simple harmonic 
oscillation become equal ?  
 (1) x = 
A
2
 (2) x = 0  (3) x = ? A  (4) x = ? 
A
2
 
Sol. (4) 
 KE = PE 
 
2 2 2
1 1
k(A – X ) KX
2 2
? 
 
2 2 2
A – X X ? 
 
2 2
2X A ? 
 
2
2
A
X
2
? 
 
A
X
2
? ? 
 
3. An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to 
that of photon is : (c being  the velocity of light)  
 (1) 
1/2
E
2m
? ?
? ?
?
?
?
? ?
? ?
  (2) 
1
c
 
1/2
E
2m
? ?
? ?
?
?
?
? ?
? ?
  (3) c(2mE)
1/2
  (4) 
1
c
1/2
2m
E
? ?
? ?
?
?
?
? ?
? ?
 
Sol. (2) 
 For photon E = 
hc
?
 
  
P
hc
E
? ? …(i) 
 For electron   
e
hc
2mE
? ? …(ii) 
 
1/2
e
2
p
hc
E 1 E
2mE
hc c 2m
2mc
E
? ? ?
? ?
? ? ? ?
?
?
? ?
? ? ?
 
 
 
4. A car accelerates from rest at a constant rate ? for some time after which it decelerates at a 
constant  rate ? to  come to rest. If the total time elapsed is t seconds, the total distance 
travelled is : ?
 (1) 
2( )
? ?
? ? ?
t
2
  (2) 
4( )
? ?
? ? ?
t
2
  (3) 
4
( )
? ?
? ? ?
t
2
  (4) 
2
( )
? ?
? ? ?
t
2
 
Sol. (1) 
 
  
 
 t
1
 + t
2
 = t, V' = 0 + ?t
1
 
 V = u + at 
 0 = ?t
1
 – ?t
2
 
 
2 1
t t
?
?
?
 
 
1 1
t t t
?
? ?
?
 
 
1
t t
? ? ?
?
? ?
? ? ?
? ?
 
  
Distance  = 
1 2 1
1
(t t ) t
2
? ? ? area of triangle 
 
1
t t
2 a
? ? ?
? ? ?
? ?
? ?
? ?
 
 
2
t
2( )
? ?
?
? ? ?
 
 
5. A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The 
amount of heat energy supplied to the engine from the source in each cycle is : 
 (1) 1800 J  (2) 3200 J  (3) 2400 J  (4) 1600 J  
Sol. (3) 
 
1
1
2
? ? ? 
 
1
2
? ? 
 ? ?
W
Q
 
 
1200 1
Q 2
? 
 Q = 2400 J 
V 
?t
1
t
1 t
2
t
 
 
17
th
 March. 2021 | Shift 1 
6. A mass M hangs  on a massless rod of length l which rotates at a constant angular frequency. 
The mass M moves with steady speed in a circular path of constant radius. Assume that the 
system is in steady circular motion with constant angular velocity ?. The angular momentum of 
M about point A is L
A
 which lies in the positive z direction and the angular momentum of M 
about point B is L
B
. The correct statement for this system is : 
 
 
M A
r
?
?
B
z
? ?
  
 (1) L
A
 and L
B
 are both constant in magnitude and direction 
 (2) L
B
 is constant, both in magnitude and direction  
 (3) L
A
 is contant, both in magnitude and direction 
  (4) L
B
 is constant  in direction with varying magnitude  
Sol. (3) 
 
x
?
v
?
L
?
r
   
 ? ?
A
L r p
?
? ?
 
 as r p ? so L
A
 = constant 
 
7. Two ideal polyatomic  gases at temperatures T
1
 and T
2
 are mixed so that there is no loss of 
energy. If F
1
 and F
2
 , m
1
 and m
2
, n
1
 and n
2
 be the degress of freedom, masses, number of  
molecules of the first and second gas respectively, the temperature of mixture  of these two 
gases is : 
 (1) 
1 1 1 2 2 2
1 1 2 2
n F T n F T
n F n F
?
?
  (2) 
1 1 1 2 2 2
1 2
n F T n F T
F F
?
?
  (3) 
1 1 1 2 2 2
1 2
n F T n F T
n n
?
?
  (4) 
1 1 2 2
1 2
n T n T
n n
?
?
  
Sol. (1) 
 initial internal energy  = final internal energy 
 
1 2 1 2
1 1 2 2 1 2
F F F F
n RT n RT n RT n RT
2 2 2 2
? ? ? 
 
1 1 1 2 2 2
1 1 2 2
F n T F n T
T
Fn F n
?
?
?
 
 
 
8. The output of the given combination gates represents : 
 
 
 
 (1) XOR Gate  (2)NOR Gate  (3) NAND Gate   (4) AND Gate  
Sol. (3) 
  
 
9. A triangular  plate is shown. A forceF
?
 = 4
ˆ
i – 3
ˆ
j is applied at point P. The torque at point P with 
respect to point 'O' and 'Q' are : 
 
 
 (1) 15 – 20 3 , 15 + 20 3  (2) 15 + 20 3 , 15 – 20 3 
  (3) –15 + 20 3 , 15 + 20 3  (4) – 15–20 3 , 15 – 20 3  
Sol. (4) 
 ? ? ? ?
0
ˆ ˆ ˆ ˆ
r (5 i 5 3 j) (4 i 3 j)
?
 
 ? ? ?
ˆ ˆ
15k 20 3k 
 
?
PQ
r = ?
? ?
0 Q
r r 
 = ? ?
ˆ ˆ ˆ
5i 5 3j 10i 
 = ? ?
ˆ ˆ
5i 5 3j 
 ? ? ?
?
? ?
Q PQ
r F 
 = 
? ? ? ?
? ? ? ?
ˆ ˆ ˆ ˆ
5i 5 3j 4i 3j 
 = ?
ˆ ˆ
15k 20 3k 
 = 
? ?
?
ˆ
15 20 3 k 
A
B
A 
B
A+B=A.B
Y =A.B
(NAND gate)
 
10cm
10cm
10cm
?
Q
r
?
O
r
?
PQ
r
O
P
Q
Y
X
60° 60°
Page 5


 
 
17
th
 March. 2021 | Shift 1 
SECTION – A 
1. The vernier scale used for measurement has a positive zero error of 0.2 mm. If while taking a 
measurement it was noted that 'o' on the vernier scale lies between 8.5 cm and 8.6 cm, vernier  
coincidence is 6, then the correct value of measurement is ……………………. cm.  
 (least count = 0.01 cm) 
 (1) 8.36 cm  (2) 8.56 cm  (3) 8.58 cm  (4) 8.54 cm 
Sol. (4) 
 Reading = MSR + VSD × LC – zero error 
 Reading = 8.5 + 
(0.1) 6 0.2
10 10
?
? =8.54 cm 
 
2. For what value of displacement the kinetic energy and potential energy of a simple harmonic 
oscillation become equal ?  
 (1) x = 
A
2
 (2) x = 0  (3) x = ? A  (4) x = ? 
A
2
 
Sol. (4) 
 KE = PE 
 
2 2 2
1 1
k(A – X ) KX
2 2
? 
 
2 2 2
A – X X ? 
 
2 2
2X A ? 
 
2
2
A
X
2
? 
 
A
X
2
? ? 
 
3. An electron of mass m and a photon have same energy E. The ratio of wavelength of electron to 
that of photon is : (c being  the velocity of light)  
 (1) 
1/2
E
2m
? ?
? ?
?
?
?
? ?
? ?
  (2) 
1
c
 
1/2
E
2m
? ?
? ?
?
?
?
? ?
? ?
  (3) c(2mE)
1/2
  (4) 
1
c
1/2
2m
E
? ?
? ?
?
?
?
? ?
? ?
 
Sol. (2) 
 For photon E = 
hc
?
 
  
P
hc
E
? ? …(i) 
 For electron   
e
hc
2mE
? ? …(ii) 
 
1/2
e
2
p
hc
E 1 E
2mE
hc c 2m
2mc
E
? ? ?
? ?
? ? ? ?
?
?
? ?
? ? ?
 
 
 
4. A car accelerates from rest at a constant rate ? for some time after which it decelerates at a 
constant  rate ? to  come to rest. If the total time elapsed is t seconds, the total distance 
travelled is : ?
 (1) 
2( )
? ?
? ? ?
t
2
  (2) 
4( )
? ?
? ? ?
t
2
  (3) 
4
( )
? ?
? ? ?
t
2
  (4) 
2
( )
? ?
? ? ?
t
2
 
Sol. (1) 
 
  
 
 t
1
 + t
2
 = t, V' = 0 + ?t
1
 
 V = u + at 
 0 = ?t
1
 – ?t
2
 
 
2 1
t t
?
?
?
 
 
1 1
t t t
?
? ?
?
 
 
1
t t
? ? ?
?
? ?
? ? ?
? ?
 
  
Distance  = 
1 2 1
1
(t t ) t
2
? ? ? area of triangle 
 
1
t t
2 a
? ? ?
? ? ?
? ?
? ?
? ?
 
 
2
t
2( )
? ?
?
? ? ?
 
 
5. A Carnot's engine working between 400 K and 800 K has a work output of 1200 J per cycle. The 
amount of heat energy supplied to the engine from the source in each cycle is : 
 (1) 1800 J  (2) 3200 J  (3) 2400 J  (4) 1600 J  
Sol. (3) 
 
1
1
2
? ? ? 
 
1
2
? ? 
 ? ?
W
Q
 
 
1200 1
Q 2
? 
 Q = 2400 J 
V 
?t
1
t
1 t
2
t
 
 
17
th
 March. 2021 | Shift 1 
6. A mass M hangs  on a massless rod of length l which rotates at a constant angular frequency. 
The mass M moves with steady speed in a circular path of constant radius. Assume that the 
system is in steady circular motion with constant angular velocity ?. The angular momentum of 
M about point A is L
A
 which lies in the positive z direction and the angular momentum of M 
about point B is L
B
. The correct statement for this system is : 
 
 
M A
r
?
?
B
z
? ?
  
 (1) L
A
 and L
B
 are both constant in magnitude and direction 
 (2) L
B
 is constant, both in magnitude and direction  
 (3) L
A
 is contant, both in magnitude and direction 
  (4) L
B
 is constant  in direction with varying magnitude  
Sol. (3) 
 
x
?
v
?
L
?
r
   
 ? ?
A
L r p
?
? ?
 
 as r p ? so L
A
 = constant 
 
7. Two ideal polyatomic  gases at temperatures T
1
 and T
2
 are mixed so that there is no loss of 
energy. If F
1
 and F
2
 , m
1
 and m
2
, n
1
 and n
2
 be the degress of freedom, masses, number of  
molecules of the first and second gas respectively, the temperature of mixture  of these two 
gases is : 
 (1) 
1 1 1 2 2 2
1 1 2 2
n F T n F T
n F n F
?
?
  (2) 
1 1 1 2 2 2
1 2
n F T n F T
F F
?
?
  (3) 
1 1 1 2 2 2
1 2
n F T n F T
n n
?
?
  (4) 
1 1 2 2
1 2
n T n T
n n
?
?
  
Sol. (1) 
 initial internal energy  = final internal energy 
 
1 2 1 2
1 1 2 2 1 2
F F F F
n RT n RT n RT n RT
2 2 2 2
? ? ? 
 
1 1 1 2 2 2
1 1 2 2
F n T F n T
T
Fn F n
?
?
?
 
 
 
8. The output of the given combination gates represents : 
 
 
 
 (1) XOR Gate  (2)NOR Gate  (3) NAND Gate   (4) AND Gate  
Sol. (3) 
  
 
9. A triangular  plate is shown. A forceF
?
 = 4
ˆ
i – 3
ˆ
j is applied at point P. The torque at point P with 
respect to point 'O' and 'Q' are : 
 
 
 (1) 15 – 20 3 , 15 + 20 3  (2) 15 + 20 3 , 15 – 20 3 
  (3) –15 + 20 3 , 15 + 20 3  (4) – 15–20 3 , 15 – 20 3  
Sol. (4) 
 ? ? ? ?
0
ˆ ˆ ˆ ˆ
r (5 i 5 3 j) (4 i 3 j)
?
 
 ? ? ?
ˆ ˆ
15k 20 3k 
 
?
PQ
r = ?
? ?
0 Q
r r 
 = ? ?
ˆ ˆ ˆ
5i 5 3j 10i 
 = ? ?
ˆ ˆ
5i 5 3j 
 ? ? ?
?
? ?
Q PQ
r F 
 = 
? ? ? ?
? ? ? ?
ˆ ˆ ˆ ˆ
5i 5 3j 4i 3j 
 = ?
ˆ ˆ
15k 20 3k 
 = 
? ?
?
ˆ
15 20 3 k 
A
B
A 
B
A+B=A.B
Y =A.B
(NAND gate)
 
10cm
10cm
10cm
?
Q
r
?
O
r
?
PQ
r
O
P
Q
Y
X
60° 60°
 
 
17
th
 March. 2021 | Shift 1 
10. A modem grand-prix racing car of mas m is travelling on a flat track in a circular arc of radius R 
with a speed v, if the coefficient of static friction between the tyres and the track is ?
s
, then the 
magnitude of negative lift F
1
 acting downwards on the car is : (Assume forces on the four tyres 
are identical and g = acceleration due to gravity) 
 
R
?
?
 (1) m
2
s
g
R
? ?
?
? ?
? ? ?
?
?
? ? ?
? ?
 (2) m
2
s
g
R
? ?
?
? ?
? ? ?
?
?
? ? ?
? ?
   (3) m
2
s
g
R
? ?
?
? ?
? ? ?
?
?
? ? ?
? ?
  (4) –m 
2
s
g
R
? ?
?
? ?
? ? ?
?
?
? ? ?
? ?
  
Sol. (1) 
 
 
f
N
mg+F
L
 
` f =
2
mv
R
 
 ?N = 
2
mv
R
 
 ?(mg + F
L
) = 
2
mv
R
 
 mg + F
L
 = 
?
2
mv
R
 
 F
L
 = 
?
2
mv
R
 - mg 
 = m 
? ?
?
? ?
?
? ?
2
v
g
R
 
 
 
11. The thickness at the centre of a plano convex lens is 3 mm and the diameter is 6 cm. If the 
speed of light in the material of the lens is 2 × 10
8
 ms
–1
. The focal length of the lens is ____. 
 (1) 0.30 cm  (2) 1.5 cm  (3) 15 cm  (4) 30 cm