JEE Advanced 2018 Solved Paper - 1 PDF Download

 Page 1


1
Answers & Solutions
for for for for for
JEE (Advanced)-2018
Time : 3 hrs. Max. Marks: 180
PAPER - 1
PART-I : PHYSICS
SECTION - 1 (Maximum Marks : 24)
? This section contains SIX(06) questions.
? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is(are) correct option(s).
? For each question, choose the correct option(s) to answer the question.
? Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (all) the correct option(s) is(are) chosen.
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of
which are correct options.
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a
correct option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –2 In all other cases.
? For example : If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any
incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option), without selecting any incorrect option (second
option in this case), will result in +1 mark. Selecting any incorrect option(s) (second option in this case),
with or without selection of any correct option(s) will result in –2 marks.
Page 2


1
Answers & Solutions
for for for for for
JEE (Advanced)-2018
Time : 3 hrs. Max. Marks: 180
PAPER - 1
PART-I : PHYSICS
SECTION - 1 (Maximum Marks : 24)
? This section contains SIX(06) questions.
? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is(are) correct option(s).
? For each question, choose the correct option(s) to answer the question.
? Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (all) the correct option(s) is(are) chosen.
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of
which are correct options.
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a
correct option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –2 In all other cases.
? For example : If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any
incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option), without selecting any incorrect option (second
option in this case), will result in +1 mark. Selecting any incorrect option(s) (second option in this case),
with or without selection of any correct option(s) will result in –2 marks.
2
JEE (ADVANCED)-2018 (PAPER-1)
1. The potential energy of a particle of mass m at a distance r from a fixed point O is given by
V(r) = 
2
kr
2
, where k is a positive constant of appropriate dimensions. This particle is moving in
a circular orbit of radius R about the point O. If v is the speed of the particle and L is the
magnitude of its angular momentum about O, which of the following statements is(are) true?
(A) ?
k
vR
2m
(B) ?
k
vR
m
(C) ?
2
LmkR (D) ?
2
mk
LR
2
Answer (B, C)
Sol.
?
dV
F–
dr
 = –kr
?
2
mv
kR
R
?
k
vR
m
L = mvR = 
2
mkR
2. Consider a body of mass 1.0 kg at rest at the origin at time t = 0. A force ?? ?? ??

ˆˆ
Fti j is applied
on the body, where ? = 1.0 Ns
–1
 and ? = 1.0 N. The torque acting on the body about the origin at
time t = 1.0 s is 
?

. Which of the following statements is(are) true?
(A)
??
 1
Nm
3
(B) The torque ?

 is in the direction of the unit vector +
ˆ
k
(C) The velocity of the body at t = 1 s is 
?? ??

–1
1
ˆˆ
vi2j ms
2
(D) The magnitude of displacement of the body at t = 1 s is 
1
m
6
Answer (A, C)
Sol. ?? ??

ˆˆ
ati j
??
??
??
??

2
t
ˆˆ
vitj
2
??
??
??
??

32
tt
ˆˆ
ri j
62
?

(t1)
v = 
?? ?
1
ˆˆ
i2j
2
?? ?

 
rf
= ??
??
?? ?
??
??
32
tt
ˆˆ ˆˆ
ij tij
62
 = 
??
??
??
33
tt
ˆ
– k
62
?
?

(t1)
 = 
1
ˆ
– Nmk
3
;  
??
 1
Nm
3
Page 3


1
Answers & Solutions
for for for for for
JEE (Advanced)-2018
Time : 3 hrs. Max. Marks: 180
PAPER - 1
PART-I : PHYSICS
SECTION - 1 (Maximum Marks : 24)
? This section contains SIX(06) questions.
? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is(are) correct option(s).
? For each question, choose the correct option(s) to answer the question.
? Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (all) the correct option(s) is(are) chosen.
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of
which are correct options.
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a
correct option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –2 In all other cases.
? For example : If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any
incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option), without selecting any incorrect option (second
option in this case), will result in +1 mark. Selecting any incorrect option(s) (second option in this case),
with or without selection of any correct option(s) will result in –2 marks.
2
JEE (ADVANCED)-2018 (PAPER-1)
1. The potential energy of a particle of mass m at a distance r from a fixed point O is given by
V(r) = 
2
kr
2
, where k is a positive constant of appropriate dimensions. This particle is moving in
a circular orbit of radius R about the point O. If v is the speed of the particle and L is the
magnitude of its angular momentum about O, which of the following statements is(are) true?
(A) ?
k
vR
2m
(B) ?
k
vR
m
(C) ?
2
LmkR (D) ?
2
mk
LR
2
Answer (B, C)
Sol.
?
dV
F–
dr
 = –kr
?
2
mv
kR
R
?
k
vR
m
L = mvR = 
2
mkR
2. Consider a body of mass 1.0 kg at rest at the origin at time t = 0. A force ?? ?? ??

ˆˆ
Fti j is applied
on the body, where ? = 1.0 Ns
–1
 and ? = 1.0 N. The torque acting on the body about the origin at
time t = 1.0 s is 
?

. Which of the following statements is(are) true?
(A)
??
 1
Nm
3
(B) The torque ?

 is in the direction of the unit vector +
ˆ
k
(C) The velocity of the body at t = 1 s is 
?? ??

–1
1
ˆˆ
vi2j ms
2
(D) The magnitude of displacement of the body at t = 1 s is 
1
m
6
Answer (A, C)
Sol. ?? ??

ˆˆ
ati j
??
??
??
??

2
t
ˆˆ
vitj
2
??
??
??
??

32
tt
ˆˆ
ri j
62
?

(t1)
v = 
?? ?
1
ˆˆ
i2j
2
?? ?

 
rf
= ??
??
?? ?
??
??
32
tt
ˆˆ ˆˆ
ij tij
62
 = 
??
??
??
33
tt
ˆ
– k
62
?
?

(t1)
 = 
1
ˆ
– Nmk
3
;  
??
 1
Nm
3
3
JEE (ADVANCED)-2018 (PAPER-1)
3. A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The
water rises to a height h in the capillary tube above the water surface in the beaker. The surface
tension of water is ?. The angle of contact between water and the wall of the capillary tube is ?.
Ignore the mass of water in the meniscus. Which of the following statements is (are) true?
(A) For a given material of the capillary tube, h decreases with increase in r
(B) For a given material of the capillary tube, h is independent of ?
(C) If this experiment is performed in a lift going up with a constant acceleration, then h
decreases
(D) h is proportional to contact angle ?
Answer (A, C)
Sol.
??
?
?
2cos
h
rg
Formula based.
4. In the figure below, the switches S
1
 and S
2
 are closed simultaneously at t = 0 and a current starts
to flow in the circuit. Both the batteries have the same magnitude of the electromotive force
(emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the
inductors. The current I in the middle wire reaches it maximum magnitude I
max
 at time t = ?. Which
of the following statements is(are) true?
(A) ?
max
V
I
2R
(B) ?
max
V
I
4R
VV
2L R L R
S
1
S
2
I
(C)
??
L
ln2
R
(D)
??
2L
ln2
R
Answer (B, D)
Sol.
?
??
??
??
??
??
tR
L
1
V
I1e
R
?
??
??
??
??
??
tR
2L
2
V
I1e
R
VV
2L R
L R
I
1
I
2
I
I = I
1
 – I
2
??
??
??
??
??
??
tR tR
2L 2L
V
Ie 1e
R
I is maximum when 
?
?
tR
2L
1
e
2
?
2L
tln2
R
?
max
V
I
4R
Page 4


1
Answers & Solutions
for for for for for
JEE (Advanced)-2018
Time : 3 hrs. Max. Marks: 180
PAPER - 1
PART-I : PHYSICS
SECTION - 1 (Maximum Marks : 24)
? This section contains SIX(06) questions.
? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is(are) correct option(s).
? For each question, choose the correct option(s) to answer the question.
? Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (all) the correct option(s) is(are) chosen.
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of
which are correct options.
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a
correct option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –2 In all other cases.
? For example : If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any
incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option), without selecting any incorrect option (second
option in this case), will result in +1 mark. Selecting any incorrect option(s) (second option in this case),
with or without selection of any correct option(s) will result in –2 marks.
2
JEE (ADVANCED)-2018 (PAPER-1)
1. The potential energy of a particle of mass m at a distance r from a fixed point O is given by
V(r) = 
2
kr
2
, where k is a positive constant of appropriate dimensions. This particle is moving in
a circular orbit of radius R about the point O. If v is the speed of the particle and L is the
magnitude of its angular momentum about O, which of the following statements is(are) true?
(A) ?
k
vR
2m
(B) ?
k
vR
m
(C) ?
2
LmkR (D) ?
2
mk
LR
2
Answer (B, C)
Sol.
?
dV
F–
dr
 = –kr
?
2
mv
kR
R
?
k
vR
m
L = mvR = 
2
mkR
2. Consider a body of mass 1.0 kg at rest at the origin at time t = 0. A force ?? ?? ??

ˆˆ
Fti j is applied
on the body, where ? = 1.0 Ns
–1
 and ? = 1.0 N. The torque acting on the body about the origin at
time t = 1.0 s is 
?

. Which of the following statements is(are) true?
(A)
??
 1
Nm
3
(B) The torque ?

 is in the direction of the unit vector +
ˆ
k
(C) The velocity of the body at t = 1 s is 
?? ??

–1
1
ˆˆ
vi2j ms
2
(D) The magnitude of displacement of the body at t = 1 s is 
1
m
6
Answer (A, C)
Sol. ?? ??

ˆˆ
ati j
??
??
??
??

2
t
ˆˆ
vitj
2
??
??
??
??

32
tt
ˆˆ
ri j
62
?

(t1)
v = 
?? ?
1
ˆˆ
i2j
2
?? ?

 
rf
= ??
??
?? ?
??
??
32
tt
ˆˆ ˆˆ
ij tij
62
 = 
??
??
??
33
tt
ˆ
– k
62
?
?

(t1)
 = 
1
ˆ
– Nmk
3
;  
??
 1
Nm
3
3
JEE (ADVANCED)-2018 (PAPER-1)
3. A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The
water rises to a height h in the capillary tube above the water surface in the beaker. The surface
tension of water is ?. The angle of contact between water and the wall of the capillary tube is ?.
Ignore the mass of water in the meniscus. Which of the following statements is (are) true?
(A) For a given material of the capillary tube, h decreases with increase in r
(B) For a given material of the capillary tube, h is independent of ?
(C) If this experiment is performed in a lift going up with a constant acceleration, then h
decreases
(D) h is proportional to contact angle ?
Answer (A, C)
Sol.
??
?
?
2cos
h
rg
Formula based.
4. In the figure below, the switches S
1
 and S
2
 are closed simultaneously at t = 0 and a current starts
to flow in the circuit. Both the batteries have the same magnitude of the electromotive force
(emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the
inductors. The current I in the middle wire reaches it maximum magnitude I
max
 at time t = ?. Which
of the following statements is(are) true?
(A) ?
max
V
I
2R
(B) ?
max
V
I
4R
VV
2L R L R
S
1
S
2
I
(C)
??
L
ln2
R
(D)
??
2L
ln2
R
Answer (B, D)
Sol.
?
??
??
??
??
??
tR
L
1
V
I1e
R
?
??
??
??
??
??
tR
2L
2
V
I1e
R
VV
2L R
L R
I
1
I
2
I
I = I
1
 – I
2
??
??
??
??
??
??
tR tR
2L 2L
V
Ie 1e
R
I is maximum when 
?
?
tR
2L
1
e
2
?
2L
tln2
R
?
max
V
I
4R
4
JEE (ADVANCED)-2018 (PAPER-1)
5. Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire located at
x = +R carries a constant current I
1
 and the wire located at x = –R carries a constant current I
2
.
A circular loop of radius R is suspended with its centre at ?? 0,0, 3R and in a plane parallel to
the xy-plane. This loop carries a constant current I in the clockwise direction as seen from above
the loop. The current in the wire is taken to be positive if it is in the +
ˆ
j direction. Which of the
following statements regarding the magnetic field 

B is(are) true?
(A) If I
1
 = I
2
, then 

B cannot be equal to zero at the origin (0, 0, 0)
(B) If I
1
 > 0 and I
2
 < 0, then 

B can be equal to zero at the origin (0, 0, 0)
(C) If I
1
 < 0 and I
2
 > 0, then 

B can be equal to zero at the origin (0, 0, 0)
(D) If I
1
 = I
2
, then the z-component of the magnetic field at the centre of the loop is 
? ??
??
??
0
I
–
2R
Answer (A, B and D)
Sol. Magnetic field due to loop at origin
?? ??
?? ?
??? ?
2
00
3
IR I
ˆˆ
kk
16R
2.8R
Magnetic field at origin due to wires
? ? ??
??
??
??
??
01 02
I I
ˆ
k
2R 2R
(A) If I
1
 = I
2
 then 
??
?
??

0
0
I
ˆ
Bk
16R
(B) It can be zero if I
1
 > 0,  I
2
 < 0
(D)
?
?
B
2
B
1
B
Loop z
I
6. One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where
V is the volume and T is the temperature). Which of the statements below is(are) true?
T
V
III
II
I
IV
(A) Process I is an isochoric process
(B) In process II, gas absorbs heat
(C) In process IV, gas releases heat
(D) Processes I and III are not isobaric
Answer (B, C, D)
Page 5


1
Answers & Solutions
for for for for for
JEE (Advanced)-2018
Time : 3 hrs. Max. Marks: 180
PAPER - 1
PART-I : PHYSICS
SECTION - 1 (Maximum Marks : 24)
? This section contains SIX(06) questions.
? Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four
option(s) is(are) correct option(s).
? For each question, choose the correct option(s) to answer the question.
? Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +4 If only (all) the correct option(s) is(are) chosen.
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of
which are correct options.
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a
correct option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –2 In all other cases.
? For example : If first, third and fourth are the ONLY three correct options for a question with second
option being an incorrect option; selecting only all the three correct options will result in +4 marks.
Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any
incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three
correct options (either first or third or fourth option), without selecting any incorrect option (second
option in this case), will result in +1 mark. Selecting any incorrect option(s) (second option in this case),
with or without selection of any correct option(s) will result in –2 marks.
2
JEE (ADVANCED)-2018 (PAPER-1)
1. The potential energy of a particle of mass m at a distance r from a fixed point O is given by
V(r) = 
2
kr
2
, where k is a positive constant of appropriate dimensions. This particle is moving in
a circular orbit of radius R about the point O. If v is the speed of the particle and L is the
magnitude of its angular momentum about O, which of the following statements is(are) true?
(A) ?
k
vR
2m
(B) ?
k
vR
m
(C) ?
2
LmkR (D) ?
2
mk
LR
2
Answer (B, C)
Sol.
?
dV
F–
dr
 = –kr
?
2
mv
kR
R
?
k
vR
m
L = mvR = 
2
mkR
2. Consider a body of mass 1.0 kg at rest at the origin at time t = 0. A force ?? ?? ??

ˆˆ
Fti j is applied
on the body, where ? = 1.0 Ns
–1
 and ? = 1.0 N. The torque acting on the body about the origin at
time t = 1.0 s is 
?

. Which of the following statements is(are) true?
(A)
??
 1
Nm
3
(B) The torque ?

 is in the direction of the unit vector +
ˆ
k
(C) The velocity of the body at t = 1 s is 
?? ??

–1
1
ˆˆ
vi2j ms
2
(D) The magnitude of displacement of the body at t = 1 s is 
1
m
6
Answer (A, C)
Sol. ?? ??

ˆˆ
ati j
??
??
??
??

2
t
ˆˆ
vitj
2
??
??
??
??

32
tt
ˆˆ
ri j
62
?

(t1)
v = 
?? ?
1
ˆˆ
i2j
2
?? ?

 
rf
= ??
??
?? ?
??
??
32
tt
ˆˆ ˆˆ
ij tij
62
 = 
??
??
??
33
tt
ˆ
– k
62
?
?

(t1)
 = 
1
ˆ
– Nmk
3
;  
??
 1
Nm
3
3
JEE (ADVANCED)-2018 (PAPER-1)
3. A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The
water rises to a height h in the capillary tube above the water surface in the beaker. The surface
tension of water is ?. The angle of contact between water and the wall of the capillary tube is ?.
Ignore the mass of water in the meniscus. Which of the following statements is (are) true?
(A) For a given material of the capillary tube, h decreases with increase in r
(B) For a given material of the capillary tube, h is independent of ?
(C) If this experiment is performed in a lift going up with a constant acceleration, then h
decreases
(D) h is proportional to contact angle ?
Answer (A, C)
Sol.
??
?
?
2cos
h
rg
Formula based.
4. In the figure below, the switches S
1
 and S
2
 are closed simultaneously at t = 0 and a current starts
to flow in the circuit. Both the batteries have the same magnitude of the electromotive force
(emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the
inductors. The current I in the middle wire reaches it maximum magnitude I
max
 at time t = ?. Which
of the following statements is(are) true?
(A) ?
max
V
I
2R
(B) ?
max
V
I
4R
VV
2L R L R
S
1
S
2
I
(C)
??
L
ln2
R
(D)
??
2L
ln2
R
Answer (B, D)
Sol.
?
??
??
??
??
??
tR
L
1
V
I1e
R
?
??
??
??
??
??
tR
2L
2
V
I1e
R
VV
2L R
L R
I
1
I
2
I
I = I
1
 – I
2
??
??
??
??
??
??
tR tR
2L 2L
V
Ie 1e
R
I is maximum when 
?
?
tR
2L
1
e
2
?
2L
tln2
R
?
max
V
I
4R
4
JEE (ADVANCED)-2018 (PAPER-1)
5. Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire located at
x = +R carries a constant current I
1
 and the wire located at x = –R carries a constant current I
2
.
A circular loop of radius R is suspended with its centre at ?? 0,0, 3R and in a plane parallel to
the xy-plane. This loop carries a constant current I in the clockwise direction as seen from above
the loop. The current in the wire is taken to be positive if it is in the +
ˆ
j direction. Which of the
following statements regarding the magnetic field 

B is(are) true?
(A) If I
1
 = I
2
, then 

B cannot be equal to zero at the origin (0, 0, 0)
(B) If I
1
 > 0 and I
2
 < 0, then 

B can be equal to zero at the origin (0, 0, 0)
(C) If I
1
 < 0 and I
2
 > 0, then 

B can be equal to zero at the origin (0, 0, 0)
(D) If I
1
 = I
2
, then the z-component of the magnetic field at the centre of the loop is 
? ??
??
??
0
I
–
2R
Answer (A, B and D)
Sol. Magnetic field due to loop at origin
?? ??
?? ?
??? ?
2
00
3
IR I
ˆˆ
kk
16R
2.8R
Magnetic field at origin due to wires
? ? ??
??
??
??
??
01 02
I I
ˆ
k
2R 2R
(A) If I
1
 = I
2
 then 
??
?
??

0
0
I
ˆ
Bk
16R
(B) It can be zero if I
1
 > 0,  I
2
 < 0
(D)
?
?
B
2
B
1
B
Loop z
I
6. One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where
V is the volume and T is the temperature). Which of the statements below is(are) true?
T
V
III
II
I
IV
(A) Process I is an isochoric process
(B) In process II, gas absorbs heat
(C) In process IV, gas releases heat
(D) Processes I and III are not isobaric
Answer (B, C, D)
5
JEE (ADVANCED)-2018 (PAPER-1)
Sol. In process II, T is constant, V is increasing.
? Q is positive, gas absorbs heat.
Similarly in process IV, gas releases heat.
In isobaric process, V ? T.
SECTION - 2 (Maximum Marks : 15)
This section contains EIGHT (08) questions. The answer to each question is a NUMERICAL VALUE.
For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the
second decimal place; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30) using the mouse and the on-screen
virtual numeric keypad in the place designated to enter the answer.
Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 If ONLY the correct numerical value is entered as answer.
Zero Marks : 0 In all other cases.
7. Two vectors 
 
AandB are defined as ?? ???
 
ˆˆˆ
AaiandB a(cos ti sin tj), where a is a constant and
?
??
6
 rad s
–1
. If ??
 
AB 3A–B at time t = ? for the first time, the value of ?, in seconds, is
_______.
Answer (2.00)
Sol.
?
??
  
t
|A B| 2acos
2
? ??
??
??
??
  
t
|A B| 2asin
2
?? ??
?
??
??
tt
2acos 3 (2a)sin
22
?
?
t1
tan
2
3
??
?
t
26
t = 2 s
8. Two men are walking along a horizontal straight line in the same direction. The man in front
walks at a speed 1.0 ms
–1
 and the man behind walks at a speed 2.0 ms
–1
. A third man is standing
at a height 12 m above the same horizontal line such that all three men are in a vertical plane.
The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz.
The speed of sound in air is 330 ms
–1
. At the instant, when the moving men are 10 m apart, the
stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary
man at this instant, is _______.
Answer (5.00)
Sol.
?? ? ? ??
?? ? ? ?? ?? ?
?? ? ? 12
ss
VV
ff ;f f
VVcos V V cos
?
?
12 m
2 m/s 1 m/s
10 m
?? ? ? ??
?? ? ? ?? ? ? ?? ? ? ?? ? ? B
330 330
f 1430 1430
55
330 2 330 1
13 13
?? ?
??
?

1430 330 13 15
5.005Hz 5.00Hz
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