Sample Solution Paper 5: Physics, Class 11

 Page 1


  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
CBSE Board 
Class XI Physics 
Sample Paper-5 Solution 
 
 
1.  
It is a fundamental unit because it is defined in terms of certain basic, though, arbitrarily 
chosen standardized reference standard. 
 
2.  
1:1, time taken is the same if air resistance is neglected. 
 
3.  
They are equal if they have the same magnitude and also the same direction.  
 
4.  
The ratio of their speeds 
21
12
vm
vm
?     
 
5.  
Impulse is the change in momentum of a body and it is given by the product of the force 
and the duration of the force 
 
6.  
A force for which the work done depends only on the end points is called a conservative 
force. 
 
7.  
At 50cm       
 
8.  
Elasticity and inertia   
 
9. 
 
1
32
2
1
3 1% 2 3% 4% 2%
2
13%
? ? ? ? ?
? ? ? ?
? ? ? ? ? ? ?
?
P a b c d
P a b c d
   
 
Page 2


  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
CBSE Board 
Class XI Physics 
Sample Paper-5 Solution 
 
 
1.  
It is a fundamental unit because it is defined in terms of certain basic, though, arbitrarily 
chosen standardized reference standard. 
 
2.  
1:1, time taken is the same if air resistance is neglected. 
 
3.  
They are equal if they have the same magnitude and also the same direction.  
 
4.  
The ratio of their speeds 
21
12
vm
vm
?     
 
5.  
Impulse is the change in momentum of a body and it is given by the product of the force 
and the duration of the force 
 
6.  
A force for which the work done depends only on the end points is called a conservative 
force. 
 
7.  
At 50cm       
 
8.  
Elasticity and inertia   
 
9. 
 
1
32
2
1
3 1% 2 3% 4% 2%
2
13%
? ? ? ? ?
? ? ? ?
? ? ? ? ? ? ?
?
P a b c d
P a b c d
   
 
  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
10. 
 
2 2 2
2
2
1
sin sin 2
2
 sin sin 2
sin 4sin cos
tan 4
tan 4
?
?
?
?
?
?
uu
gg
Hence
??
??
? ? ?
?
?
 
OR 
 
2
ˆ ˆ ˆ ˆ
( ) (3.0 2.0 ) 3.0 4.0
ˆ
( ) 4.0
? ? ? ?
?
d
v t ti t j i tj
dt
a t j
 
 
11. 
Since work done (W) = f s cos ?  
Work done by the cycle on the road is zero because the displacement of the road is zero. 
  
12.  
The angle between these vectors is 180 degrees as they are in opposite direction to each 
other.  
The right hand screw rule gives the direction. Open up your right hand palm and curl the 
fingers pointing from vector a to vector b. Your outstretched thumb points in the direction 
of the vector product. 
 
13.  
The various regions of the spherical shell attract the point mass inside it in various 
directions. These forces cancel each other out completely so the net force on a point mass 
inside it is zero.  
 
14. 
 
52
5
92
/
0.01
100
2 2 1.013 10 /
2 1.013 10
2.026 10 /
0.01
100
?
?
?
?
?
? ? ? ? ?
??
? ? ?
p
B
VV
V
V
p atmospheres N m
B N m
 
 
 
 
Page 3


  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
CBSE Board 
Class XI Physics 
Sample Paper-5 Solution 
 
 
1.  
It is a fundamental unit because it is defined in terms of certain basic, though, arbitrarily 
chosen standardized reference standard. 
 
2.  
1:1, time taken is the same if air resistance is neglected. 
 
3.  
They are equal if they have the same magnitude and also the same direction.  
 
4.  
The ratio of their speeds 
21
12
vm
vm
?     
 
5.  
Impulse is the change in momentum of a body and it is given by the product of the force 
and the duration of the force 
 
6.  
A force for which the work done depends only on the end points is called a conservative 
force. 
 
7.  
At 50cm       
 
8.  
Elasticity and inertia   
 
9. 
 
1
32
2
1
3 1% 2 3% 4% 2%
2
13%
? ? ? ? ?
? ? ? ?
? ? ? ? ? ? ?
?
P a b c d
P a b c d
   
 
  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
10. 
 
2 2 2
2
2
1
sin sin 2
2
 sin sin 2
sin 4sin cos
tan 4
tan 4
?
?
?
?
?
?
uu
gg
Hence
??
??
? ? ?
?
?
 
OR 
 
2
ˆ ˆ ˆ ˆ
( ) (3.0 2.0 ) 3.0 4.0
ˆ
( ) 4.0
? ? ? ?
?
d
v t ti t j i tj
dt
a t j
 
 
11. 
Since work done (W) = f s cos ?  
Work done by the cycle on the road is zero because the displacement of the road is zero. 
  
12.  
The angle between these vectors is 180 degrees as they are in opposite direction to each 
other.  
The right hand screw rule gives the direction. Open up your right hand palm and curl the 
fingers pointing from vector a to vector b. Your outstretched thumb points in the direction 
of the vector product. 
 
13.  
The various regions of the spherical shell attract the point mass inside it in various 
directions. These forces cancel each other out completely so the net force on a point mass 
inside it is zero.  
 
14. 
 
52
5
92
/
0.01
100
2 2 1.013 10 /
2 1.013 10
2.026 10 /
0.01
100
?
?
?
?
?
? ? ? ? ?
??
? ? ?
p
B
VV
V
V
p atmospheres N m
B N m
 
 
 
 
  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
15.  
It states that the rate of cooling of a body is proportional to the excess temperature of the 
body over the surroundings. 
 
21
()
dQ
k T T
dt
?? 
Where T 1 is the temperature of the surrounding medium and T 2 is the temperature of the 
body.     
 
16. 
 
12
12
12
12
3 1
12
2
33
39.9
(273 20) 2.52 10
4
??
?
? ? ? ? ? ?
rms
RT RT
v
MM
TT
MM
M
T T K
M
 
 
17. 
 
2
i)At maximum height v=0
0 = usin -gt
2usin
Time of flight T = 2t = 
g
) The body falls back to the same height at which it started when
it covers its horizontal range. Then derive 
u sin 2
R = 
ii
g
?
?
?
 
18. 
 
2
11
2
11
12
1f 1
12
2
1
12
1
1 1 2
1
The initial kinetic energy of the neutron = 
2
1
 final kinetic energy of the neutron = 
2
 v
 fractional kinetic energy lost is
f
 ki
?
?
?
?? ?
??
??
?
??
i
f
i
f
i
mv
The mv
mm
Use v
mm
The
K
mm
K m m
Fractional
? ?
2
1 2 1 2
21 2
12
12
netic energy gained by the nuclei with which it collides is
4
f 1 1
?? ?
? ? ? ? ?
??
?
?
??
m m mm
f
mm
mm
 
If 
12
 and m m are comparable with each other, the energy transferred is more. 
Page 4


  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
CBSE Board 
Class XI Physics 
Sample Paper-5 Solution 
 
 
1.  
It is a fundamental unit because it is defined in terms of certain basic, though, arbitrarily 
chosen standardized reference standard. 
 
2.  
1:1, time taken is the same if air resistance is neglected. 
 
3.  
They are equal if they have the same magnitude and also the same direction.  
 
4.  
The ratio of their speeds 
21
12
vm
vm
?     
 
5.  
Impulse is the change in momentum of a body and it is given by the product of the force 
and the duration of the force 
 
6.  
A force for which the work done depends only on the end points is called a conservative 
force. 
 
7.  
At 50cm       
 
8.  
Elasticity and inertia   
 
9. 
 
1
32
2
1
3 1% 2 3% 4% 2%
2
13%
? ? ? ? ?
? ? ? ?
? ? ? ? ? ? ?
?
P a b c d
P a b c d
   
 
  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
10. 
 
2 2 2
2
2
1
sin sin 2
2
 sin sin 2
sin 4sin cos
tan 4
tan 4
?
?
?
?
?
?
uu
gg
Hence
??
??
? ? ?
?
?
 
OR 
 
2
ˆ ˆ ˆ ˆ
( ) (3.0 2.0 ) 3.0 4.0
ˆ
( ) 4.0
? ? ? ?
?
d
v t ti t j i tj
dt
a t j
 
 
11. 
Since work done (W) = f s cos ?  
Work done by the cycle on the road is zero because the displacement of the road is zero. 
  
12.  
The angle between these vectors is 180 degrees as they are in opposite direction to each 
other.  
The right hand screw rule gives the direction. Open up your right hand palm and curl the 
fingers pointing from vector a to vector b. Your outstretched thumb points in the direction 
of the vector product. 
 
13.  
The various regions of the spherical shell attract the point mass inside it in various 
directions. These forces cancel each other out completely so the net force on a point mass 
inside it is zero.  
 
14. 
 
52
5
92
/
0.01
100
2 2 1.013 10 /
2 1.013 10
2.026 10 /
0.01
100
?
?
?
?
?
? ? ? ? ?
??
? ? ?
p
B
VV
V
V
p atmospheres N m
B N m
 
 
 
 
  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
15.  
It states that the rate of cooling of a body is proportional to the excess temperature of the 
body over the surroundings. 
 
21
()
dQ
k T T
dt
?? 
Where T 1 is the temperature of the surrounding medium and T 2 is the temperature of the 
body.     
 
16. 
 
12
12
12
12
3 1
12
2
33
39.9
(273 20) 2.52 10
4
??
?
? ? ? ? ? ?
rms
RT RT
v
MM
TT
MM
M
T T K
M
 
 
17. 
 
2
i)At maximum height v=0
0 = usin -gt
2usin
Time of flight T = 2t = 
g
) The body falls back to the same height at which it started when
it covers its horizontal range. Then derive 
u sin 2
R = 
ii
g
?
?
?
 
18. 
 
2
11
2
11
12
1f 1
12
2
1
12
1
1 1 2
1
The initial kinetic energy of the neutron = 
2
1
 final kinetic energy of the neutron = 
2
 v
 fractional kinetic energy lost is
f
 ki
?
?
?
?? ?
??
??
?
??
i
f
i
f
i
mv
The mv
mm
Use v
mm
The
K
mm
K m m
Fractional
? ?
2
1 2 1 2
21 2
12
12
netic energy gained by the nuclei with which it collides is
4
f 1 1
?? ?
? ? ? ? ?
??
?
?
??
m m mm
f
mm
mm
 
If 
12
 and m m are comparable with each other, the energy transferred is more. 
  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
19.  
The moment of inertia of a rigid body about an axis defined by the formula 
2
i
 where r
ii
I mr ?
?
 is the perpendicular distance of the i
th
 point of the body from the axis. 
 
The moment of inertial about a tangent to the ring in the plane of the ring is the moment of 
inertia about a diameter parallel to the tangent + Mh
2
 where h is the distance between the 
two parallel axes. 
 
 I = MR
2
/2 + MR
2
 = 3/2 MR
2 
 
 
20.  
The change in total energy is  
 
9
2( ) 2( ) 4
2( ) 2( 3 ) 8
Change in total energy = 3.13 10 J
88
?
? ? ? ? ? ?
??
? ? ? ? ? ?
??
? ? ?
fi
i
f
EE
GmM GmM GmM
E
R h R R R
GmM GmM GmM
E
R h R R R
GmM gmR
R
 
 
The kinetic energy of the satellite reduces and it is given by
9
3.13 10 J ?? .  
The change is potential energy is twice the change in the total energy so change in potential 
energy is
9
6.26 10 J ?? . 
 
21.  
(a) From the given graphs we observe that for a given strain, stress required for A is 
more than that of B. Hence, Young's Modulus (= Stress/strain) of A is greater than that 
of B. 
(b) Material A is stronger as it can withstand more stress (load) before breaking 
(fracture) of the material. 
OR 
Pascal’s law states that whenever external pressure is applied on any part of a fluid 
contained in a vessel, it is transmitted undiminished and equally in all directions.  
Pressure = atmospheric pressure + pressure due to the water.   
 
55
1.01 10 10(1000)(10) 2.01 10 P Pa ? ? ? ? ?   
 
Page 5


  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
CBSE Board 
Class XI Physics 
Sample Paper-5 Solution 
 
 
1.  
It is a fundamental unit because it is defined in terms of certain basic, though, arbitrarily 
chosen standardized reference standard. 
 
2.  
1:1, time taken is the same if air resistance is neglected. 
 
3.  
They are equal if they have the same magnitude and also the same direction.  
 
4.  
The ratio of their speeds 
21
12
vm
vm
?     
 
5.  
Impulse is the change in momentum of a body and it is given by the product of the force 
and the duration of the force 
 
6.  
A force for which the work done depends only on the end points is called a conservative 
force. 
 
7.  
At 50cm       
 
8.  
Elasticity and inertia   
 
9. 
 
1
32
2
1
3 1% 2 3% 4% 2%
2
13%
? ? ? ? ?
? ? ? ?
? ? ? ? ? ? ?
?
P a b c d
P a b c d
   
 
  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
10. 
 
2 2 2
2
2
1
sin sin 2
2
 sin sin 2
sin 4sin cos
tan 4
tan 4
?
?
?
?
?
?
uu
gg
Hence
??
??
? ? ?
?
?
 
OR 
 
2
ˆ ˆ ˆ ˆ
( ) (3.0 2.0 ) 3.0 4.0
ˆ
( ) 4.0
? ? ? ?
?
d
v t ti t j i tj
dt
a t j
 
 
11. 
Since work done (W) = f s cos ?  
Work done by the cycle on the road is zero because the displacement of the road is zero. 
  
12.  
The angle between these vectors is 180 degrees as they are in opposite direction to each 
other.  
The right hand screw rule gives the direction. Open up your right hand palm and curl the 
fingers pointing from vector a to vector b. Your outstretched thumb points in the direction 
of the vector product. 
 
13.  
The various regions of the spherical shell attract the point mass inside it in various 
directions. These forces cancel each other out completely so the net force on a point mass 
inside it is zero.  
 
14. 
 
52
5
92
/
0.01
100
2 2 1.013 10 /
2 1.013 10
2.026 10 /
0.01
100
?
?
?
?
?
? ? ? ? ?
??
? ? ?
p
B
VV
V
V
p atmospheres N m
B N m
 
 
 
 
  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
15.  
It states that the rate of cooling of a body is proportional to the excess temperature of the 
body over the surroundings. 
 
21
()
dQ
k T T
dt
?? 
Where T 1 is the temperature of the surrounding medium and T 2 is the temperature of the 
body.     
 
16. 
 
12
12
12
12
3 1
12
2
33
39.9
(273 20) 2.52 10
4
??
?
? ? ? ? ? ?
rms
RT RT
v
MM
TT
MM
M
T T K
M
 
 
17. 
 
2
i)At maximum height v=0
0 = usin -gt
2usin
Time of flight T = 2t = 
g
) The body falls back to the same height at which it started when
it covers its horizontal range. Then derive 
u sin 2
R = 
ii
g
?
?
?
 
18. 
 
2
11
2
11
12
1f 1
12
2
1
12
1
1 1 2
1
The initial kinetic energy of the neutron = 
2
1
 final kinetic energy of the neutron = 
2
 v
 fractional kinetic energy lost is
f
 ki
?
?
?
?? ?
??
??
?
??
i
f
i
f
i
mv
The mv
mm
Use v
mm
The
K
mm
K m m
Fractional
? ?
2
1 2 1 2
21 2
12
12
netic energy gained by the nuclei with which it collides is
4
f 1 1
?? ?
? ? ? ? ?
??
?
?
??
m m mm
f
mm
mm
 
If 
12
 and m m are comparable with each other, the energy transferred is more. 
  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
19.  
The moment of inertia of a rigid body about an axis defined by the formula 
2
i
 where r
ii
I mr ?
?
 is the perpendicular distance of the i
th
 point of the body from the axis. 
 
The moment of inertial about a tangent to the ring in the plane of the ring is the moment of 
inertia about a diameter parallel to the tangent + Mh
2
 where h is the distance between the 
two parallel axes. 
 
 I = MR
2
/2 + MR
2
 = 3/2 MR
2 
 
 
20.  
The change in total energy is  
 
9
2( ) 2( ) 4
2( ) 2( 3 ) 8
Change in total energy = 3.13 10 J
88
?
? ? ? ? ? ?
??
? ? ? ? ? ?
??
? ? ?
fi
i
f
EE
GmM GmM GmM
E
R h R R R
GmM GmM GmM
E
R h R R R
GmM gmR
R
 
 
The kinetic energy of the satellite reduces and it is given by
9
3.13 10 J ?? .  
The change is potential energy is twice the change in the total energy so change in potential 
energy is
9
6.26 10 J ?? . 
 
21.  
(a) From the given graphs we observe that for a given strain, stress required for A is 
more than that of B. Hence, Young's Modulus (= Stress/strain) of A is greater than that 
of B. 
(b) Material A is stronger as it can withstand more stress (load) before breaking 
(fracture) of the material. 
OR 
Pascal’s law states that whenever external pressure is applied on any part of a fluid 
contained in a vessel, it is transmitted undiminished and equally in all directions.  
Pressure = atmospheric pressure + pressure due to the water.   
 
55
1.01 10 10(1000)(10) 2.01 10 P Pa ? ? ? ? ?   
 
  
 
CBSE  | Physics  
Sample Paper 5 Solution 
 
     
22.  
In equilibrium, the total energy is equally distributed in all possible energy modes, with 
each mode having an average energy equal to 1/2kT. This is the law of equipartition of 
energy. 
 
A diatomic molecule that can be taken as a rigid rotator with 5 degrees of freedom: 3 
translational and 2 rotational. Using the law of equipartition of energy the total internal 
energy of a mole of such a gas is given by  
 
V
P
P
V
55
 
22
5
Then molar specific heat at constant volume C
2
7
 molar specific heat at constant pressure C
2
C 7
 
C5
? ? ?
?
?
?
U kT N RT
R
and R
Hence
 
 
23.  
If both are travelling towards north then relative velocity of car A w.r.t. B is 60-45 = 
15km/h northwards.    
 
If A travels towards north and B travels southwards then velocity of A w.r.t. B is 60-(-45) = 
105km/h northwards.     
 
24.  
Work-energy theorem states that the work done on a particle by a resultant force is equal 
to the change in its kinetic energy.  
 
21
. . .
. . .
??
? ? ?
??
??
? ? ?
ds
W F ds F dt
dt
dK
Fvdt dt dK
dt
W K K
 
 
25.  
We know that, 
 
dP
F
dt
?     or    Fdt dP ?    
 
If the impact lasts for a small time dt and the momentum of the body changes from
12
PtoP 
then,