16. Two solid circular shafts of radii R₁ and R₂ are subjected to same torque. The maximum shear stresses developed in the two shafts are τ₁ and τ₂. If R₁/R₂ = 2, then τ₂/τ₁ is ______.

1. 1. 8

   
   
   

   2. 8.1

   
   
   

   3. 7.9

   
   
   

   4. 8.2

   
   
   

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   R1	= 2
   R2

   
   T₁ = T₂.
   

   =		τJ			+		τJ
   		r		1			r		2

   
   

   τ1d41	=	τ2d42
   d1		d2

   
   

   τ1	=	d³2	=	1
   τ1		d³1		8

   
   d₁d₂
   

   τ2	= 8
   τ1

   Correct Option: A

   R1	= 2
   R2

   
   T₁ = T₂.
   

   =		τJ			+		τJ
   		r		1			r		2

   
   

   τ1d41	=	τ2d42
   d1		d2

   
   

   τ1	=	d³2	=	1
   τ1		d³1		8

   
   d₁d₂
   

   τ2	= 8
   τ1

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17. Consider a stepped shaft subjected to a twisting moment applied at B as shown in the figure. Assume shear modulus, G = 77 GPa. The angle of twist at C (in degree) is _______.
    

1. 1. 1

   
   
   

   2. 0.236050

   
   
   

   3. 2.236356

   
   
   

   4. 1.936050

   
   
   

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1. View Hint View Answer Discuss in Forum

   Angle of twist at (C) = Angle of twist at (B)
   

   ⇒ θ =	TL
   	GJ

   
   

   ⇒	10 × 0.5 × 32
   	77 × 109 × π × .024

   
   ⇒ 0.236050

   Correct Option: A

   Angle of twist at (C) = Angle of twist at (B)
   

   ⇒ θ =	TL
   	GJ

   
   

   ⇒	10 × 0.5 × 32
   	77 × 109 × π × .024

   
   ⇒ 0.236050

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18. A hollow shaft (d₀ = 2d_i where d₀ and d_i are the outer and inner diameters respectively) needs to transmit 20 kW power at 3000 RPM. If the maximum permissible shear stress is 30 MPa, d₀ is

1. 1. 11.29 mm

   
   
   

   2. 22.58 mm

   
   
   

   3. 33.87 mm

   
   
   

   4. 45.16 mm

   
   
   

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   P = Tω
   

   20 × 10³ = T ×	2π × 3000
   	60

   
   ∴ T = 63.662 N– m
   

   Now	T	=	τ
   	Ip		r

   
   

   So,	63.662	=	30 × 106	(r0 = d),
   	π/32(15d41)		d1

   
   ∴ d₁ = 11.295 mm
   ∴ d₀ = 2d₁ = 22.59 mm

   Correct Option: B

   P = Tω
   

   20 × 10³ = T ×	2π × 3000
   	60

   
   ∴ T = 63.662 N– m
   

   Now	T	=	τ
   	Ip		r

   
   

   So,	63.662	=	30 × 106	(r0 = d),
   	π/32(15d41)		d1

   
   ∴ d₁ = 11.295 mm
   ∴ d₀ = 2d₁ = 22.59 mm

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19. A frame is subjected to a load P as shown in the figure. The frame has a constant flexural rigidity EI. The effect of axial load is neglected. The deflection at point A due to the applied load P is
    

1. 1. 1PL³
      3EI

   
   
   

   2. 2PL³
      3EI

   
   
   

   3. PL4
      EI

   
   
   

   4. 4PL³
      3EI

   
   
   

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   Strain energy (t) = L∫0	M²xdx	+ L∫0	M²ydx
   	2EI		2EI

   
   M_x = P_x    M_yP_y
   

   1	Pδ = L∫0	(px)²dx	+ L∫0	(px)²dx
   2		2EI		2EI

   
   

   =	2	P²L²	=	1	P ×	4	PL³
   	3	EI		2		3	EI

   
   

   δ =	4	PL³
   	3	EI

   Correct Option: D

   Strain energy (t) = L∫0	M²xdx	+ L∫0	M²ydx
   	2EI		2EI

   
   M_x = P_x    M_yP_y
   

   1	Pδ = L∫0	(px)²dx	+ L∫0	(px)²dx
   2		2EI		2EI

   
   

   =	2	P²L²	=	1	P ×	4	PL³
   	3	EI		2		3	EI

   
   

   δ =	4	PL³
   	3	EI

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20. A simply supported beam of length 2L is subjected to a moment M at the mid-point x = 0 as shown in the figure. The deflection in the domain 0 < x < L is given by
    

    w =	- Mx	(L - x)(x + c)
    	12EIL

    
    where E is the Young's modulus, I is the area moment of inertia and C is a constant (to be determined).
    

1. 1. ML
      (2EI)

   
   
   

   2. ML
      (3EI)

   
   
   

   3. ML
      (6EI)

   
   
   

   4. ML
      (12EI)

   
   
   

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   ΔBA =	(first moment area APB)
   	EI

   
   
   

   =	-1		M	×	1	× L × 2	L		M
   	EI		2		2		3		2EI

   
   

   =	ML²
   	6EI

   
   

   Slope at A =	ΔBA	=	ML
   	L		6EI

   Correct Option: C

   ΔBA =	(first moment area APB)
   	EI

   
   
   

   =	-1		M	×	1	× L × 2	L		M
   	EI		2		2		3		2EI

   
   

   =	ML²
   	6EI

   
   

   Slope at A =	ΔBA	=	ML
   	L		6EI

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