Page 1
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
1. A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. the fragments having
equal masses fly off along mutually perpendicular direction with speed V. What will be the speed of the third (lighter) fragment?
A.
From conservation of momentum
1
O2mv 2 mv =+
V
1
= 22v 
Hence, velocity of third part is 22v at an angle of 135
o
with either part.
2. A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. A T what height will the ball lose
contact with surface of the sphere ?
A. If the ball lose contact at B then, from conservation of energy.
mg cos?
mg sin?
R
R cos = h ?
R  R cos ?
N
mV
2
R
A
V
()
2
1
mgR 1 cos mv
2
?=
v
2
= 2gR (1 – cos?) ......(i)
At B
2
mV
N mg cos
R
+= ?
When the ball will lose the contact
N = O
2
mv
mg cos
R
?=
DESCRIPTIVE TYPE QUESTIONS
SUB : PHYSICS & CHEMISTRY
Page 2
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
1. A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. the fragments having
equal masses fly off along mutually perpendicular direction with speed V. What will be the speed of the third (lighter) fragment?
A.
From conservation of momentum
1
O2mv 2 mv =+
V
1
= 22v 
Hence, velocity of third part is 22v at an angle of 135
o
with either part.
2. A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. A T what height will the ball lose
contact with surface of the sphere ?
A. If the ball lose contact at B then, from conservation of energy.
mg cos?
mg sin?
R
R cos = h ?
R  R cos ?
N
mV
2
R
A
V
()
2
1
mgR 1 cos mv
2
?=
v
2
= 2gR (1 – cos?) ......(i)
At B
2
mV
N mg cos
R
+= ?
When the ball will lose the contact
N = O
2
mv
mg cos
R
?=
DESCRIPTIVE TYPE QUESTIONS
SUB : PHYSICS & CHEMISTRY
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
V
2
= gR cos ? ........(ii)
? from (i) & (ii)
2Rg(1  cos ) = gRcos ??
2 – 2 cos ? = cos ?.
2 = 3 cos ?.
? Height from the ground
h = R cos ? =
2R
3
3. Two identical cylindrical vessels, with their bases at the same level, each cotain a liquid of density p. The height of liquid in one
vessel in h
1
and that in the other is h
2
. The area of either base is A. What is the work done by gravity in equalizing the levels
when the vessles are interconnected ?
A.
P
h
1
A A h
2
?
Let find height = h
12
hh
h
2
+ ??
?=
??
??
decerese in height
12 1 2
1
hh h h
hh
22
+ ??? ?
?=  =
??? ?
??? ?
Mass of liquid
( )
12
hh
mA
2

=?
? Work done
12 12
hh hh
WA
22
? ?  ?? ? ?
=?
?? ?? ??
?? ? ? ??
=
()
2
12
hh
gA
4

?
4. A battery of emf E and internal resistance r is connected across a pure resistive device (such as an electric heater) of resistance
R. Prove that the power output of the device will be maximum if R = r.
A. I
R
r
E
E
I
Rr
=
+
Page 3
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
1. A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. the fragments having
equal masses fly off along mutually perpendicular direction with speed V. What will be the speed of the third (lighter) fragment?
A.
From conservation of momentum
1
O2mv 2 mv =+
V
1
= 22v 
Hence, velocity of third part is 22v at an angle of 135
o
with either part.
2. A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. A T what height will the ball lose
contact with surface of the sphere ?
A. If the ball lose contact at B then, from conservation of energy.
mg cos?
mg sin?
R
R cos = h ?
R  R cos ?
N
mV
2
R
A
V
()
2
1
mgR 1 cos mv
2
?=
v
2
= 2gR (1 – cos?) ......(i)
At B
2
mV
N mg cos
R
+= ?
When the ball will lose the contact
N = O
2
mv
mg cos
R
?=
DESCRIPTIVE TYPE QUESTIONS
SUB : PHYSICS & CHEMISTRY
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
V
2
= gR cos ? ........(ii)
? from (i) & (ii)
2Rg(1  cos ) = gRcos ??
2 – 2 cos ? = cos ?.
2 = 3 cos ?.
? Height from the ground
h = R cos ? =
2R
3
3. Two identical cylindrical vessels, with their bases at the same level, each cotain a liquid of density p. The height of liquid in one
vessel in h
1
and that in the other is h
2
. The area of either base is A. What is the work done by gravity in equalizing the levels
when the vessles are interconnected ?
A.
P
h
1
A A h
2
?
Let find height = h
12
hh
h
2
+ ??
?=
??
??
decerese in height
12 1 2
1
hh h h
hh
22
+ ??? ?
?=  =
??? ?
??? ?
Mass of liquid
( )
12
hh
mA
2

=?
? Work done
12 12
hh hh
WA
22
? ?  ?? ? ?
=?
?? ?? ??
?? ? ? ??
=
()
2
12
hh
gA
4

?
4. A battery of emf E and internal resistance r is connected across a pure resistive device (such as an electric heater) of resistance
R. Prove that the power output of the device will be maximum if R = r.
A. I
R
r
E
E
I
Rr
=
+
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
Power P = I
2
R =
()
2
2
ER
Rr +
For maximum power
dp
0
dR
=
() ()
()
2
2
Rr .1 R.2Rr
E0
Rr4
??
+ +
= ??
+
??
??
R + r – 2R = 0
r = R
5. A radioactive isotope X with half life 1.5 × 10
9
yrs. decays into a stable nucleus Y . A rock sample contains both elements X and
Y in ratio 1 : 15. Find the age of the rock.
A.
X Y
t = 0, 16 0
t = 1, 1 15
9
1
2
T 1.5 10 yr =×
n
o
1
NN
2
??
=
??
??
1 = 16
n
1
2
??
??
??
n4
11
n4
22
?? ? ?
=?=
?? ? ?
?? ? ?
? time t = 4 × 1.5 × 10
9
= 6 ×10
9
yrs
6. The bacterial growth follows the rate l aw,
dN
KN
dt
=
where ‘K’ is a constant and ‘N’ is the number of bacteria cell at any time.
If the population of bacteria (no. of cell) is doubled in 5 minutes, find the time by which the population will be eight times of the
initial one.
A.
dN
KN
dt
=
(1st order kinetics)
? N = N
0
e
kt
(integrating)
? in 5 min, N = 2N
0
0
2.303 N
Klog
tN
=
Page 4
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
1. A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. the fragments having
equal masses fly off along mutually perpendicular direction with speed V. What will be the speed of the third (lighter) fragment?
A.
From conservation of momentum
1
O2mv 2 mv =+
V
1
= 22v 
Hence, velocity of third part is 22v at an angle of 135
o
with either part.
2. A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. A T what height will the ball lose
contact with surface of the sphere ?
A. If the ball lose contact at B then, from conservation of energy.
mg cos?
mg sin?
R
R cos = h ?
R  R cos ?
N
mV
2
R
A
V
()
2
1
mgR 1 cos mv
2
?=
v
2
= 2gR (1 – cos?) ......(i)
At B
2
mV
N mg cos
R
+= ?
When the ball will lose the contact
N = O
2
mv
mg cos
R
?=
DESCRIPTIVE TYPE QUESTIONS
SUB : PHYSICS & CHEMISTRY
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
V
2
= gR cos ? ........(ii)
? from (i) & (ii)
2Rg(1  cos ) = gRcos ??
2 – 2 cos ? = cos ?.
2 = 3 cos ?.
? Height from the ground
h = R cos ? =
2R
3
3. Two identical cylindrical vessels, with their bases at the same level, each cotain a liquid of density p. The height of liquid in one
vessel in h
1
and that in the other is h
2
. The area of either base is A. What is the work done by gravity in equalizing the levels
when the vessles are interconnected ?
A.
P
h
1
A A h
2
?
Let find height = h
12
hh
h
2
+ ??
?=
??
??
decerese in height
12 1 2
1
hh h h
hh
22
+ ??? ?
?=  =
??? ?
??? ?
Mass of liquid
( )
12
hh
mA
2

=?
? Work done
12 12
hh hh
WA
22
? ?  ?? ? ?
=?
?? ?? ??
?? ? ? ??
=
()
2
12
hh
gA
4

?
4. A battery of emf E and internal resistance r is connected across a pure resistive device (such as an electric heater) of resistance
R. Prove that the power output of the device will be maximum if R = r.
A. I
R
r
E
E
I
Rr
=
+
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
Power P = I
2
R =
()
2
2
ER
Rr +
For maximum power
dp
0
dR
=
() ()
()
2
2
Rr .1 R.2Rr
E0
Rr4
??
+ +
= ??
+
??
??
R + r – 2R = 0
r = R
5. A radioactive isotope X with half life 1.5 × 10
9
yrs. decays into a stable nucleus Y . A rock sample contains both elements X and
Y in ratio 1 : 15. Find the age of the rock.
A.
X Y
t = 0, 16 0
t = 1, 1 15
9
1
2
T 1.5 10 yr =×
n
o
1
NN
2
??
=
??
??
1 = 16
n
1
2
??
??
??
n4
11
n4
22
?? ? ?
=?=
?? ? ?
?? ? ?
? time t = 4 × 1.5 × 10
9
= 6 ×10
9
yrs
6. The bacterial growth follows the rate l aw,
dN
KN
dt
=
where ‘K’ is a constant and ‘N’ is the number of bacteria cell at any time.
If the population of bacteria (no. of cell) is doubled in 5 minutes, find the time by which the population will be eight times of the
initial one.
A.
dN
KN
dt
=
(1st order kinetics)
? N = N
0
e
kt
(integrating)
? in 5 min, N = 2N
0
0
2.303 N
Klog
tN
=
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
?
o
0
2N 2.303
Klog
5N
??
=
??
??
min
–1
?
2.303
Klog2
5
=
for 8N
0
o
o
8N 2.303
tlog
2.303
N
log 2
5
??
??
=
??
??
??
??
?
53log2
t15min
log 2
×
==
? time required is 15 min.
7. In ‘x’ ml 0.3 (N) HCl, addition of 200 ml distilled water or addition of 100 ml 0.1 (N) NaOH, gives same final acid strength.
Determine ‘x’.
A. When 200 ml H
2
O is added to x ml solution
(x) (0.3) = (x + 200) (Y) ? final conc.
Y =
0.3x
200 x +
in 2nd case
Number of equivalents of HCl after NaOH addition
0.3x
0.01
1000

( no of eq. of NaOH added = 0.01)
? conc. would be
0.3x
0.01
1000
1000(N)
100 x
??

??
??
×
+
by condition,
0.3x
0.01 1000
0.3x 1000
100 x 200 x
??

??
??
=
++
?
0.3x 10 0.3x
100 x (200 x)

=
++
? (0.3x – 10) × (200 + x) = (0.3x)(100 +x)
? 60x – 2000 + 0.3 x
2
– 10x = 30x + 0.3x
2
? 20x = 2000 ? x = 100 ml
8. Compound A treated with NaNH
2
followed by CH
3
CH
2
Br gave compound B. Partial hydrogenation of compound B produced
compound C, which on ozonolysis gave a carbonyl compound D, (C
3
H
6
O). Compound D did not respond to iodoform test with
I
2
/Kl and NaOH. Find out the structures of A, B, C and D
A. Assuming 1 eq. of NaNH
2
is used,
Page 5
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
1. A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio 2 : 2 : 1. the fragments having
equal masses fly off along mutually perpendicular direction with speed V. What will be the speed of the third (lighter) fragment?
A.
From conservation of momentum
1
O2mv 2 mv =+
V
1
= 22v 
Hence, velocity of third part is 22v at an angle of 135
o
with either part.
2. A small spherical ball of mass m slides without friction from the top of a hemisphere of radius R. A T what height will the ball lose
contact with surface of the sphere ?
A. If the ball lose contact at B then, from conservation of energy.
mg cos?
mg sin?
R
R cos = h ?
R  R cos ?
N
mV
2
R
A
V
()
2
1
mgR 1 cos mv
2
?=
v
2
= 2gR (1 – cos?) ......(i)
At B
2
mV
N mg cos
R
+= ?
When the ball will lose the contact
N = O
2
mv
mg cos
R
?=
DESCRIPTIVE TYPE QUESTIONS
SUB : PHYSICS & CHEMISTRY
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
V
2
= gR cos ? ........(ii)
? from (i) & (ii)
2Rg(1  cos ) = gRcos ??
2 – 2 cos ? = cos ?.
2 = 3 cos ?.
? Height from the ground
h = R cos ? =
2R
3
3. Two identical cylindrical vessels, with their bases at the same level, each cotain a liquid of density p. The height of liquid in one
vessel in h
1
and that in the other is h
2
. The area of either base is A. What is the work done by gravity in equalizing the levels
when the vessles are interconnected ?
A.
P
h
1
A A h
2
?
Let find height = h
12
hh
h
2
+ ??
?=
??
??
decerese in height
12 1 2
1
hh h h
hh
22
+ ??? ?
?=  =
??? ?
??? ?
Mass of liquid
( )
12
hh
mA
2

=?
? Work done
12 12
hh hh
WA
22
? ?  ?? ? ?
=?
?? ?? ??
?? ? ? ??
=
()
2
12
hh
gA
4

?
4. A battery of emf E and internal resistance r is connected across a pure resistive device (such as an electric heater) of resistance
R. Prove that the power output of the device will be maximum if R = r.
A. I
R
r
E
E
I
Rr
=
+
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
Power P = I
2
R =
()
2
2
ER
Rr +
For maximum power
dp
0
dR
=
() ()
()
2
2
Rr .1 R.2Rr
E0
Rr4
??
+ +
= ??
+
??
??
R + r – 2R = 0
r = R
5. A radioactive isotope X with half life 1.5 × 10
9
yrs. decays into a stable nucleus Y . A rock sample contains both elements X and
Y in ratio 1 : 15. Find the age of the rock.
A.
X Y
t = 0, 16 0
t = 1, 1 15
9
1
2
T 1.5 10 yr =×
n
o
1
NN
2
??
=
??
??
1 = 16
n
1
2
??
??
??
n4
11
n4
22
?? ? ?
=?=
?? ? ?
?? ? ?
? time t = 4 × 1.5 × 10
9
= 6 ×10
9
yrs
6. The bacterial growth follows the rate l aw,
dN
KN
dt
=
where ‘K’ is a constant and ‘N’ is the number of bacteria cell at any time.
If the population of bacteria (no. of cell) is doubled in 5 minutes, find the time by which the population will be eight times of the
initial one.
A.
dN
KN
dt
=
(1st order kinetics)
? N = N
0
e
kt
(integrating)
? in 5 min, N = 2N
0
0
2.303 N
Klog
tN
=
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
?
o
0
2N 2.303
Klog
5N
??
=
??
??
min
–1
?
2.303
Klog2
5
=
for 8N
0
o
o
8N 2.303
tlog
2.303
N
log 2
5
??
??
=
??
??
??
??
?
53log2
t15min
log 2
×
==
? time required is 15 min.
7. In ‘x’ ml 0.3 (N) HCl, addition of 200 ml distilled water or addition of 100 ml 0.1 (N) NaOH, gives same final acid strength.
Determine ‘x’.
A. When 200 ml H
2
O is added to x ml solution
(x) (0.3) = (x + 200) (Y) ? final conc.
Y =
0.3x
200 x +
in 2nd case
Number of equivalents of HCl after NaOH addition
0.3x
0.01
1000

( no of eq. of NaOH added = 0.01)
? conc. would be
0.3x
0.01
1000
1000(N)
100 x
??

??
??
×
+
by condition,
0.3x
0.01 1000
0.3x 1000
100 x 200 x
??

??
??
=
++
?
0.3x 10 0.3x
100 x (200 x)

=
++
? (0.3x – 10) × (200 + x) = (0.3x)(100 +x)
? 60x – 2000 + 0.3 x
2
– 10x = 30x + 0.3x
2
? 20x = 2000 ? x = 100 ml
8. Compound A treated with NaNH
2
followed by CH
3
CH
2
Br gave compound B. Partial hydrogenation of compound B produced
compound C, which on ozonolysis gave a carbonyl compound D, (C
3
H
6
O). Compound D did not respond to iodoform test with
I
2
/Kl and NaOH. Find out the structures of A, B, C and D
A. Assuming 1 eq. of NaNH
2
is used,
WBJEE  2011 (Hints & Solutions) Physics & Chemistry
CH CH C CH =
3 2
NaNH
2
– NH
3
CH CH C C Na =
3 2
– +
CH CH – Br
3 2
S+
S–
S
N
2
? – NaBr
CH
3
CH
2
CH = CH CH
2
CH
3
Partial
Hydrogenation
????? ? CH
3
CH
2
C = C–CH
2
CH
3
(C) (B)
(i) O
(ii) Zn + H O
2
3
Ozonolysis
2 CH
3
CH
2
CHO (No Keto Methyl group ? –ve iodoform)
(D)
9. An organic compound with molecular formula C
9
H
10
O forms, 2, 4DNP derivative, reduces Tollen’s reagent and undergoes
Cannizzaro reaction. On vigorous oxidation it gives a dicarboxylic acid which is used in the preparation of terylene. Identify the
organic compound.
A. +ve Brady’s test indicates carbonyl compound, Tollens & Cannizzaro reaction indicates aldehyde without a – H
? end product is terepthalic acid, compound must be
CHO
CH CH
3 2
[Strong oxidation]
COOH
COOH
(Terepthalic acid)
pethylbenzaldehyde
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