36. An offset slider-crank mechanism is shown in the figure at an instant. Conventionally, the Quick Return Ratio (QRR) is considered to be greater than one. The value of QRR is ______.
    

1. 1. 255

   
   
   

   2. 1.255

   
   
   

   3. 5.255

   
   
   

   4. 1255

   
   
   

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1. View Hint View Answer Discuss in Forum

   AB = stroke length
   AO = 40 – 20 = 20
   BO = 40 + 20 = 60
   ∠ AOB = ∠ BOC – ∠ AOC
   = 80.41 – 60 = 20.41
   

   QRR =	180 + φ	=	180 + 20.41	= 1.255.
   	180 − φ		180 − 20.41

   
   

   Correct Option: B

   AB = stroke length
   AO = 40 – 20 = 20
   BO = 40 + 20 = 60
   ∠ AOB = ∠ BOC – ∠ AOC
   = 80.41 – 60 = 20.41
   

   QRR =	180 + φ	=	180 + 20.41	= 1.255.
   	180 − φ		180 − 20.41

   
   

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37. Consider the triangular formed by the connecting rod and the crank of an IC engine as the two sides of the triangle. If the maximum area of this triangle occurs when the crank is 75°, the ratio of connecting rod length to crank radius to

1. 1. 5

   
   
   

   2. 4

   
   
   

   3. 3.73

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Δ =	1	(PQ) (PR) sin A
   	2

   
   Area will be maximum when A = 90°
   i.e. PQR is a right angled triangle.
   ∴  Ratio of connecting rod length to crank radius,
   

   l	= tan 75° = 3.732;
   r

   
   l = 3.732 r
   

   Correct Option: C

   Δ =	1	(PQ) (PR) sin A
   	2

   
   Area will be maximum when A = 90°
   i.e. PQR is a right angled triangle.
   ∴  Ratio of connecting rod length to crank radius,
   

   l	= tan 75° = 3.732;
   r

   
   l = 3.732 r
   

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38. The cross head velocity in the slider crank mechanism, for the position shown in figure
    

1. 1. V_ccos(90 − α + β)cosβ

   
   
   

   2. V_ccos(90 − α + β)secβ

   
   
   

   3. V_ccos(90 − α − β)cosβ

   
   
   

   4. V_ccos(90 − α − β)secβ

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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39. A rigid rod of length 1 m is resting at an angle θ = 45° as shown in the figure. The end P is dragged with a velocity of U = 5 m/s to the right. At the instant shown, the magnitude of the velocity V(in m/s) of point Q as it moves along the wall without losing contact is
    

1. 1. 5

   
   
   

   2. 6

   
   
   

   3. 8

   
   
   

   4. 10

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   V_P = r _Pω
   ⇒  5 = 1 × sin 45° × ω
   

   ⇒  ω =	5
   	1 × sin45°

   
   V_Q = r _Qω
   

   ⇒  VQ = 1 × cos45° ×	5
   	1 × sin45°

   
   = 5 m/s

   Correct Option: A

   
   V_P = r _Pω
   ⇒  5 = 1 × sin 45° × ω
   

   ⇒  ω =	5
   	1 × sin45°

   
   V_Q = r _Qω
   

   ⇒  VQ = 1 × cos45° ×	5
   	1 × sin45°

   
   = 5 m/s

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40. A rigid link PQ is undergoing plane motion as shown in the figure (V_P and V_Q are non-zero). V_QP is the relative velocity of point Q with respect to point P
    
    Which one of the following is TRUE?

1. 1. V_QP has components along and perpendicular to PQ

   
   
   

   2. V_QP has only one component directed from P to Q

   
   
   

   3. V_QP has only one component directed from Q to P

   
   
   

   4. V_QP has only one component perpendicular to PQ

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Resultant V_QP is ⊥_r to link PQ.

   Correct Option: D

   
   Resultant V_QP is ⊥_r to link PQ.

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