41. A rod of length L and diameter D is subjected to a tensile load P. Which of the following is sufficient to calculate the resulting change in diameter?

1. 1. Young's modulus

   
   
   

   2. Shear modulus

   
   
   

   3. Poisson's ratio

   
   
   

   4. Both Young's modulus and shear modulus

   
   
   

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1. View Hint View Answer Discuss in Forum

   Both Young's modulus and shear modulus

   Correct Option: D

   Both Young's modulus and shear modulus

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42. A 200 × 100 × 50 mm steel block is subjected to a hydro static pressure of 15 MPa. The Young's modulus and Poisson's ratio of the material are 200 GPa and 0.3 respectively. The change in the volume of the block in mm³ is

1. 1. 85

   
   
   

   2. 90

   
   
   

   3. 100

   
   
   

   4. 110

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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43. In terms of Poisson's ratio (μ) the ratio of Young's modulus (E) to Shear modulus (G) of elastic materials is

1. 1. 2(1 + μ)

   
   
   

   2. 2 (1– μ)

   
   
   

   3. 	1	(1 + μ)
      	2

   
   
   

   4. 	1	(1 - μ)
      	2

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know E = 2G[1 + v]
   E/G = 2[1 + v].
   
   18. Here, P_x = P_x = P_x = – 15 × 10⁶ Pa
   (compression)
   

   Now, ex	Px	=	Py	=	Pz	= 3 × 10-5
   	T2		2π		π

   
   where, m = Poisson’s ratio
   e_x = e_y = e_z = 3 × 10^-5
   e_x + e_y + e_z = 9 × 10^-5
   ∴ Change in volume = Total strain × Original = 90 m³

   Correct Option: A

   We know E = 2G[1 + v]
   E/G = 2[1 + v].
   
   18. Here, P_x = P_x = P_x = – 15 × 10⁶ Pa
   (compression)
   

   Now, ex	Px	=	Py	=	Pz	= 3 × 10-5
   	T2		2π		π

   
   where, m = Poisson’s ratio
   e_x = e_y = e_z = 3 × 10^-5
   e_x + e_y + e_z = 9 × 10^-5
   ∴ Change in volume = Total strain × Original = 90 m³

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44. If the wire diameter of a compressive helical spring is increased by 2%, the change in spring stiffness (in%) is _______ (correct to two decimal places.)

1. 1. 8.243%

   
   
   

   2. 24%

   
   
   

   3. 3%

   
   
   

   4. 43%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Stiffness of helical spring
   

   k =	Gd4
   	64R3 n

   
   ∴ k ∝ d⁴
   

   	k'	=		d'		4
   	k			d

   
   

   k' =		1.02 d		4	k
   		d

   
   k' = 1.08243 k
   

   % increase in k =	k' - k	× 100%
   	k

   
   

   =		1.08243 k - k		× 100% = 8.243%
   		k

   Correct Option: A

   Stiffness of helical spring
   

   k =	Gd4
   	64R3 n

   
   ∴ k ∝ d⁴
   

   	k'	=		d'		4
   	k			d

   
   

   k' =		1.02 d		4	k
   		d

   
   k' = 1.08243 k
   

   % increase in k =	k' - k	× 100%
   	k

   
   

   =		1.08243 k - k		× 100% = 8.243%
   		k

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45. A helical compression spring made of a wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is 24 MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is ___.

1. 1. 6

   
   
   

   2. 9

   
   
   

   3. 1

   
   
   

   4. 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   τmax =	8WD	kw
   	πd2

   
   

   τmax ∝	1
   	d2

   
   [ ∴ W₁ = W₂ = W ; C₁ = C₂ ; ( K_w)₁ = ( K_w)₂ = ( K_w) ]
   

   	τ2	=		d1		2
   	τ1			d2

   
   

   	τ2	=		d		2
   	24			2d

   
   ⇒ τ₂ = 6 MPa

   Correct Option: A

   τmax =	8WD	kw
   	πd2

   
   

   τmax ∝	1
   	d2

   
   [ ∴ W₁ = W₂ = W ; C₁ = C₂ ; ( K_w)₁ = ( K_w)₂ = ( K_w) ]
   

   	τ2	=		d1		2
   	τ1			d2

   
   

   	τ2	=		d		2
   	24			2d

   
   ⇒ τ₂ = 6 MPa

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