1. In a statically determinate plane truss, the number of joints (j) and the number of members (m) are related by
   

1. 1. j = 2m – 3
      

   
   
   

   2. m = 2j + 1
      

   
   
   

   3. m = 2j – 3
      

   
   
   

   4. m = 2j – 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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2. Which of the following statements is INCORRECT?

1. 1. Grashofs rule states that for a planar crankrocker four bar mechanism, the sum of the shortest and longest link lengths cannot be less than the sum of the remaining two link lengths.

   
   
   

   2. Inversions of a mechanism are created by fixing different links one at a time.

   
   
   

   3. Geneva mechanism is an intermittent motion device.

   
   
   

   4. Grubler's criterion assumes mobility of a planar mechanism to be one.

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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3. A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP= 2.7 m with all revolute joints. The link to be fixed to obtain rocker (rocker-rocker) mechanism is
   

1. 1. PQ
      

   
   
   

   2. QR
      

   
   
   

   3. RS
      

   
   
   

   4. SP

   
   
   

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   The link opposite to shortest link is fixed.

   Correct Option: C

   The link opposite to shortest link is fixed.

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4. Match the approaches given below to perform stated kinematics/dynamics analysis of machine.
   

   Analysis	Approach
   P. Continuous	1. D' Alembert's principle relative rotation
   Q. Velocity and	2. Grubler's criterion acceleration
   R. Mobility	3. Grashof's law
   S. Dynamic - static	4. Kennedy's theorem analysis

   
   

1. 1. P-1, Q-2, R-3, S-4
      

   
   
   

   2. P-3, Q-4, R-2, S-1
      

   
   
   

   3. P-2, Q-3, R-4, S-1
      

   
   
   

   4. P-4, Q-2, R-1, S-3

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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5. The velocity of point B with respect to point A is a vector of magnitude
   

1. 1. 0
      

   
   
   

   2. ω(r_B – r_A) and direction opposite to the direction of motion of point B
      

   
   
   

   3. ω(r_B – r_A) and direction same as the direction of motion of point B.
      

   
   
   

   4. ω²(r_B – r_A) and direction being from O to Z
      

   
   
   

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   B has the linear velocity ω_B r_B
   A has the linear velocity ω_A r_A
   
   Obviously, ω_B r_B > ω_A r_A
   because ω_A = ω_B = ω and r_B > r_A
   ∴ ωr_B > ωr_A
   So relative velocity = ω(r_B – r_A) in the direction of motion of point B.
   and, it will experience a centripetal acceleration of ω² (r_B – r_A) towards “O”
   

   Correct Option: C

   B has the linear velocity ω_B r_B
   A has the linear velocity ω_A r_A
   
   Obviously, ω_B r_B > ω_A r_A
   because ω_A = ω_B = ω and r_B > r_A
   ∴ ωr_B > ωr_A
   So relative velocity = ω(r_B – r_A) in the direction of motion of point B.
   and, it will experience a centripetal acceleration of ω² (r_B – r_A) towards “O”
   

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