31. The input link O₂P of a four bar linkage is rotated at 2 rad/s in counter clockwise direction as shown below. The angular velocity of the coupler PQ in rad/s, at an instant when ∠O₄O₂P = 180°, is
    
    PQ = Q₄Q = √2a
    O₂P = O₂O₄ = a

1. 1. 4

   
   
   

   2. 2√2

   
   
   

   3. 1

   
   
   

   4. 1√2

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   When ∠O₄O₂ P = 180°
   

   Now,	ω3	=	I12I23	=	a
   	ω2		I12I23		2a

   
   

   	ω3	=	1
   	2		2

   
   ω₃ = 1 rad/s

   Correct Option: C

   
   When ∠O₄O₂ P = 180°
   

   Now,	ω3	=	I12I23	=	a
   	ω2		I12I23		2a

   
   

   	ω3	=	1
   	2		2

   
   ω₃ = 1 rad/s

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32. In a four-bar linkage, S denotes the shortest link length, L is the longest link length, P and Q are the lengths of other two links. At least one of the three moving links will rotate by 360° if

1. 1. S + L ≤ P + Q

   
   
   

   2. S + L > P + Q

   
   
   

   3. S + P ≤ L + Q

   
   
   

   4. S + P > L + Q

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to Grashoff’s Criteria.
   S + L ≤ P + Q

   Correct Option: A

   According to Grashoff’s Criteria.
   S + L ≤ P + Q

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33. For a mechanism shown below, the mechanical advantage for the given configuration is
    

1. 1. 0.0

   
   
   

   2. 0.5

   
   
   

   3. 1.0

   
   
   

   4. ∞

   
   
   

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1. View Hint View Answer Discuss in Forum

   Mechanical advantage =	Load (output force)
   	Effort (input force)

   
   For a four bar linkage in toggle position, effort = 0
   ∴  Mechanical Advantage = ∞

   Correct Option: A

   Mechanical advantage =	Load (output force)
   	Effort (input force)

   
   For a four bar linkage in toggle position, effort = 0
   ∴  Mechanical Advantage = ∞

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34. In a certain slider-crank mechanism, lengths of crank and connecting rod are equal. If the crank rotates with a uniform angular speed of 14 rad/s and the crank length is 300 mm, the maximum acceleration of the slider (in m/s2) is _________.

1. 1. 112.6 m/s²

   
   
   

   2. 117 m/s²

   
   
   

   3. 117.6 m/s²

   
   
   

   4. 7.6 m/s²

   
   
   

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1. View Hint View Answer Discuss in Forum

   a_max = 2rω²
   (where θ = 0) i.e at Inner dead centre
   = 2 × 0.3 × 14²
   a_max = 117.6 m/s²

   Correct Option: C

   a_max = 2rω²
   (where θ = 0) i.e at Inner dead centre
   = 2 × 0.3 × 14²
   a_max = 117.6 m/s²

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35. A slider-crank mechanism with crank radius 60 mm and connecting rod length 240 mm is shown in figure. The crank is rotating with a uniform angular speed of 10 rad/s, counter clockwise. For the given configuration, the speed (in m/s) of the slider is _______.
    

1. 1. 0.6 m/s

   
   
   

   2. 0.3 m/s

   
   
   

   3. 0.1 m/s

   
   
   

   4. 0.1 m/s

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   L = 240 mm
   r = 60 mm
   

   n =	L	= 4
   	r

   
   ω = 10 rad/s
   

   cosθ =	sinθ
   	n

   
   θ = tan⁻¹(4) = 75.96°
   

   ∴  VS = ωr		sinθ +	sin2θ
   			2n

   
   

   ∴  VS = 10 × 0.06		sin75.96° +	sin151.92°
   			2 × 4

   
   = 0.6 × 1.0288
   = 0.6 m/s

   Correct Option: A

   
   L = 240 mm
   r = 60 mm
   

   n =	L	= 4
   	r

   
   ω = 10 rad/s
   

   cosθ =	sinθ
   	n

   
   θ = tan⁻¹(4) = 75.96°
   

   ∴  VS = ωr		sinθ +	sin2θ
   			2n

   
   

   ∴  VS = 10 × 0.06		sin75.96° +	sin151.92°
   			2 × 4

   
   = 0.6 × 1.0288
   = 0.6 m/s

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