DC Pandey Solutions (JEE Advance): Elasticity | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
  (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
  (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
  (c) If Assertion is true, but the Reason is false. 
  (d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : Steel is more elastic than rubber. 
  Reason : For same strain, steel requires more stress to be produced in it. 
Q 2.  Assertion : If pressure is increased, bulk modulus of gases will increase.  
  Reason : With increase in pressure, temperature of gas also increases. 
Q 3.  Assertion: From the relation 
Fl
Y
Al
?
?
, we can say that, if length of a wire is doubled, its Young's 
modulus of elasticity will also becomes two times.  
  Reason : Modulus of elasticity is a material property. 
Q 4.  Assertion : Bulk modulus of elasticity can be defined for all three states of matter, solid liquid and 
gas. 
  Reason : Young's modulus is not defined for liquids and gases. 
Q 5.  Assertion : Every wire is like a spring, whose spring constant, K ? 
1
l
 
where l is length of wire. 
  Reason : It follows from the relation 
YA
K
l
? 
Q 6.  Assertion : Ratio of stress and strain is always constant for a substance.  
  Reason : This ratio is called modulus of elasticity. 
Q 7.  Assertion : Ratio of isothermal bulk modulus and adiabatic bulk modulus for a monoatomic gas 
 at a given pressure is 
3
5
.
 
 
  Reason : This ratio is equal to 
p
V
C
C
?? . 
Answers 
1. (a) 2. (c) 3. (d) 4. (b) 5. (a) 6. (d) 7. (c) 
Solutions 
1.  Elasticity depends upon Young's modulus, which is more for steel as more stress is required to 
produce same strain, i.e., reason is true explanation of assertion. 
2.  Assertion and reason are both false as Bulk modulus of gas depends upon thermodynamic process, 
while the relation between pressure and temperature also depends upon thermodynamic process. 
3.  Assertion is false as Young's modulus do not depend upon length while reason is true. 
4.  Assertion and reason are both true but not correct explanation. 
5.  Reason truly explains assertion. 
6.  Assertion is not true as it is true only with in elastic limit. 
Page 2


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
  (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
  (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
  (c) If Assertion is true, but the Reason is false. 
  (d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : Steel is more elastic than rubber. 
  Reason : For same strain, steel requires more stress to be produced in it. 
Q 2.  Assertion : If pressure is increased, bulk modulus of gases will increase.  
  Reason : With increase in pressure, temperature of gas also increases. 
Q 3.  Assertion: From the relation 
Fl
Y
Al
?
?
, we can say that, if length of a wire is doubled, its Young's 
modulus of elasticity will also becomes two times.  
  Reason : Modulus of elasticity is a material property. 
Q 4.  Assertion : Bulk modulus of elasticity can be defined for all three states of matter, solid liquid and 
gas. 
  Reason : Young's modulus is not defined for liquids and gases. 
Q 5.  Assertion : Every wire is like a spring, whose spring constant, K ? 
1
l
 
where l is length of wire. 
  Reason : It follows from the relation 
YA
K
l
? 
Q 6.  Assertion : Ratio of stress and strain is always constant for a substance.  
  Reason : This ratio is called modulus of elasticity. 
Q 7.  Assertion : Ratio of isothermal bulk modulus and adiabatic bulk modulus for a monoatomic gas 
 at a given pressure is 
3
5
.
 
 
  Reason : This ratio is equal to 
p
V
C
C
?? . 
Answers 
1. (a) 2. (c) 3. (d) 4. (b) 5. (a) 6. (d) 7. (c) 
Solutions 
1.  Elasticity depends upon Young's modulus, which is more for steel as more stress is required to 
produce same strain, i.e., reason is true explanation of assertion. 
2.  Assertion and reason are both false as Bulk modulus of gas depends upon thermodynamic process, 
while the relation between pressure and temperature also depends upon thermodynamic process. 
3.  Assertion is false as Young's modulus do not depend upon length while reason is true. 
4.  Assertion and reason are both true but not correct explanation. 
5.  Reason truly explains assertion. 
6.  Assertion is not true as it is true only with in elastic limit. 
7.   is true and reason is also true but not correct explanation. 
 
  More than One Correct Options 
Q 1.  A metal wire of length L, area of cross-section A. and Young's modulus Y is stretched by a 
variable force F such that F is always slightly greater than the elastic forces of resistance in the 
wire. When the elongation of the wire is l 
  (a) the work done by F is 
2
YAl
2L
  
(b) the work done by F is 
2
YAl
L 
  (c) the elastic potential energy stored in the wire is 
2
YAl
2L
 
  (d) the elastic potential energy stored in the wire is 
2
YAl
4L
 
Q 2.  Two wires A and B of same length are made of same material. The figure represents the load F 
versus extension ?x graph for the two wires. Then : 
 
  (a) The cross sectional area of A is greater than that of B 
  (b) The elasticity of B is greater than that of A 
  (c) The cross-sectional area of B is greater than that of A 
  (d) The elasticity of A is greater than that of B 
Q 3.  A body of mass M is attached to the lower end of a metal wire, whose upper end is fixed. The 
elongation of the wire is l. 
  (a) Loss in gravitational potential energy of M is Mgl 
  (b) The elastic potential energy stored in the wire is Mgl 
  (c) The elastic potential energy stored in the wire is 
1
Mgl
2
 
  (d) Heat produced is 
1
Mgl
2
 
Answers 
1. (a,c) 2. (c) 3. (a,c,d) 
Solutions 
1.  dW = F . dx = kx dx =  xdx 
    
2.  
  From graph, mA < m B 
Page 3


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
  (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
  (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
  (c) If Assertion is true, but the Reason is false. 
  (d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : Steel is more elastic than rubber. 
  Reason : For same strain, steel requires more stress to be produced in it. 
Q 2.  Assertion : If pressure is increased, bulk modulus of gases will increase.  
  Reason : With increase in pressure, temperature of gas also increases. 
Q 3.  Assertion: From the relation 
Fl
Y
Al
?
?
, we can say that, if length of a wire is doubled, its Young's 
modulus of elasticity will also becomes two times.  
  Reason : Modulus of elasticity is a material property. 
Q 4.  Assertion : Bulk modulus of elasticity can be defined for all three states of matter, solid liquid and 
gas. 
  Reason : Young's modulus is not defined for liquids and gases. 
Q 5.  Assertion : Every wire is like a spring, whose spring constant, K ? 
1
l
 
where l is length of wire. 
  Reason : It follows from the relation 
YA
K
l
? 
Q 6.  Assertion : Ratio of stress and strain is always constant for a substance.  
  Reason : This ratio is called modulus of elasticity. 
Q 7.  Assertion : Ratio of isothermal bulk modulus and adiabatic bulk modulus for a monoatomic gas 
 at a given pressure is 
3
5
.
 
 
  Reason : This ratio is equal to 
p
V
C
C
?? . 
Answers 
1. (a) 2. (c) 3. (d) 4. (b) 5. (a) 6. (d) 7. (c) 
Solutions 
1.  Elasticity depends upon Young's modulus, which is more for steel as more stress is required to 
produce same strain, i.e., reason is true explanation of assertion. 
2.  Assertion and reason are both false as Bulk modulus of gas depends upon thermodynamic process, 
while the relation between pressure and temperature also depends upon thermodynamic process. 
3.  Assertion is false as Young's modulus do not depend upon length while reason is true. 
4.  Assertion and reason are both true but not correct explanation. 
5.  Reason truly explains assertion. 
6.  Assertion is not true as it is true only with in elastic limit. 
7.   is true and reason is also true but not correct explanation. 
 
  More than One Correct Options 
Q 1.  A metal wire of length L, area of cross-section A. and Young's modulus Y is stretched by a 
variable force F such that F is always slightly greater than the elastic forces of resistance in the 
wire. When the elongation of the wire is l 
  (a) the work done by F is 
2
YAl
2L
  
(b) the work done by F is 
2
YAl
L 
  (c) the elastic potential energy stored in the wire is 
2
YAl
2L
 
  (d) the elastic potential energy stored in the wire is 
2
YAl
4L
 
Q 2.  Two wires A and B of same length are made of same material. The figure represents the load F 
versus extension ?x graph for the two wires. Then : 
 
  (a) The cross sectional area of A is greater than that of B 
  (b) The elasticity of B is greater than that of A 
  (c) The cross-sectional area of B is greater than that of A 
  (d) The elasticity of A is greater than that of B 
Q 3.  A body of mass M is attached to the lower end of a metal wire, whose upper end is fixed. The 
elongation of the wire is l. 
  (a) Loss in gravitational potential energy of M is Mgl 
  (b) The elastic potential energy stored in the wire is Mgl 
  (c) The elastic potential energy stored in the wire is 
1
Mgl
2
 
  (d) Heat produced is 
1
Mgl
2
 
Answers 
1. (a,c) 2. (c) 3. (a,c,d) 
Solutions 
1.  dW = F . dx = kx dx =  xdx 
    
2.  
  From graph, mA < m B 
    
  it is possible when, YA < YB or 
   AA < AB or LA > LB but as YA = YB 
   and LA = LB ? AA < A B 
3.  W g = Mg . l, 
  Q = W g - U =  Mgl 
 
  Match the Columns  
Q 1.  Match the following two columns, (dimension wise) 
Column I Column II 
(a) Stress  (p) coefficient of friction 
(b) Strain  (q) relative density 
(c) Modulus of elasticity  (r) energy density 
(d) Force constant of a wire  (s) None 
Q 2.  A wire of length l, area of cross section A and Young's modulus of elasticity Y is stretched by a 
longitudinal force F. The change in length is Match the following two columns. 
  Note In column I, corresponding to every option, other factors remain constant. 
Column I Column II 
(a) F is increased (p) ?l will increase 
(b) l is increased  (q) stress will increase 
(c) A is increased  (r) ?l will decrease 
(d) Y is increased (s) stress will decrease 
Answers 
  1. (a) ? r (b) ? p,q (c) ? r (d) ? s  2. (a) ? pq (b) ? p (c) ? rs (d) ? r 
Solutions 
1.  (a) [stress] = [F] / [A] = [MLT
-2
L
-2
 ] = [ML
-1
T
-2
]  
 
   = [ML
-1
T
-2
] r
2  
  
(b) [strain] = ?l/l = [M
0
L
0
T
0
] ? p, q 
  (c) 
   = [ML
-1
T
-2
] ? r  
  (d) F = kx 
   
   = [MLT
-2
L
-1
] = [MT
-2
] ? s 
 2.  
Page 4


For JEE Advanced 
  Assertion and Reason 
  Directions : Choose the correct option. 
  (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
  (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
  (c) If Assertion is true, but the Reason is false. 
  (d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : Steel is more elastic than rubber. 
  Reason : For same strain, steel requires more stress to be produced in it. 
Q 2.  Assertion : If pressure is increased, bulk modulus of gases will increase.  
  Reason : With increase in pressure, temperature of gas also increases. 
Q 3.  Assertion: From the relation 
Fl
Y
Al
?
?
, we can say that, if length of a wire is doubled, its Young's 
modulus of elasticity will also becomes two times.  
  Reason : Modulus of elasticity is a material property. 
Q 4.  Assertion : Bulk modulus of elasticity can be defined for all three states of matter, solid liquid and 
gas. 
  Reason : Young's modulus is not defined for liquids and gases. 
Q 5.  Assertion : Every wire is like a spring, whose spring constant, K ? 
1
l
 
where l is length of wire. 
  Reason : It follows from the relation 
YA
K
l
? 
Q 6.  Assertion : Ratio of stress and strain is always constant for a substance.  
  Reason : This ratio is called modulus of elasticity. 
Q 7.  Assertion : Ratio of isothermal bulk modulus and adiabatic bulk modulus for a monoatomic gas 
 at a given pressure is 
3
5
.
 
 
  Reason : This ratio is equal to 
p
V
C
C
?? . 
Answers 
1. (a) 2. (c) 3. (d) 4. (b) 5. (a) 6. (d) 7. (c) 
Solutions 
1.  Elasticity depends upon Young's modulus, which is more for steel as more stress is required to 
produce same strain, i.e., reason is true explanation of assertion. 
2.  Assertion and reason are both false as Bulk modulus of gas depends upon thermodynamic process, 
while the relation between pressure and temperature also depends upon thermodynamic process. 
3.  Assertion is false as Young's modulus do not depend upon length while reason is true. 
4.  Assertion and reason are both true but not correct explanation. 
5.  Reason truly explains assertion. 
6.  Assertion is not true as it is true only with in elastic limit. 
7.   is true and reason is also true but not correct explanation. 
 
  More than One Correct Options 
Q 1.  A metal wire of length L, area of cross-section A. and Young's modulus Y is stretched by a 
variable force F such that F is always slightly greater than the elastic forces of resistance in the 
wire. When the elongation of the wire is l 
  (a) the work done by F is 
2
YAl
2L
  
(b) the work done by F is 
2
YAl
L 
  (c) the elastic potential energy stored in the wire is 
2
YAl
2L
 
  (d) the elastic potential energy stored in the wire is 
2
YAl
4L
 
Q 2.  Two wires A and B of same length are made of same material. The figure represents the load F 
versus extension ?x graph for the two wires. Then : 
 
  (a) The cross sectional area of A is greater than that of B 
  (b) The elasticity of B is greater than that of A 
  (c) The cross-sectional area of B is greater than that of A 
  (d) The elasticity of A is greater than that of B 
Q 3.  A body of mass M is attached to the lower end of a metal wire, whose upper end is fixed. The 
elongation of the wire is l. 
  (a) Loss in gravitational potential energy of M is Mgl 
  (b) The elastic potential energy stored in the wire is Mgl 
  (c) The elastic potential energy stored in the wire is 
1
Mgl
2
 
  (d) Heat produced is 
1
Mgl
2
 
Answers 
1. (a,c) 2. (c) 3. (a,c,d) 
Solutions 
1.  dW = F . dx = kx dx =  xdx 
    
2.  
  From graph, mA < m B 
    
  it is possible when, YA < YB or 
   AA < AB or LA > LB but as YA = YB 
   and LA = LB ? AA < A B 
3.  W g = Mg . l, 
  Q = W g - U =  Mgl 
 
  Match the Columns  
Q 1.  Match the following two columns, (dimension wise) 
Column I Column II 
(a) Stress  (p) coefficient of friction 
(b) Strain  (q) relative density 
(c) Modulus of elasticity  (r) energy density 
(d) Force constant of a wire  (s) None 
Q 2.  A wire of length l, area of cross section A and Young's modulus of elasticity Y is stretched by a 
longitudinal force F. The change in length is Match the following two columns. 
  Note In column I, corresponding to every option, other factors remain constant. 
Column I Column II 
(a) F is increased (p) ?l will increase 
(b) l is increased  (q) stress will increase 
(c) A is increased  (r) ?l will decrease 
(d) Y is increased (s) stress will decrease 
Answers 
  1. (a) ? r (b) ? p,q (c) ? r (d) ? s  2. (a) ? pq (b) ? p (c) ? rs (d) ? r 
Solutions 
1.  (a) [stress] = [F] / [A] = [MLT
-2
L
-2
 ] = [ML
-1
T
-2
]  
 
   = [ML
-1
T
-2
] r
2  
  
(b) [strain] = ?l/l = [M
0
L
0
T
0
] ? p, q 
  (c) 
   = [ML
-1
T
-2
] ? r  
  (d) F = kx 
   
   = [MLT
-2
L
-1
] = [MT
-2
] ? s 
 2.  
  (a)  
  (b)   
  (c)  
  (d)