36. A rigid rod (AB) of length L = √2 m is undergoing translational as well as rotational motion in the x-y plane (see the figure). The point A has the velocity V₁ = i + 2j m/s. The end B is constrained to move only along the x direction.
    
    The magnitude of the velocity V₂ (in m/s) at the end B is __________.

1. 1. 3m/s

   
   
   

   2. 2m/s

   
   
   

   3. 4m/s

   
   
   

   4. 1m/s

   
   
   

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1. View Hint View Answer Discuss in Forum

   V₁ = i + 2j
   |V₁| = √2² + 1² = √5
   By drawing velocity diagram
   
   

   α = tan-1			2			= 63.44
   			1

   
   By applying sine rule
   

   		√5	=	V2
   		sin 45		sin 71.57

   
   ∴ V₂ = 3 m/sec

   Correct Option: A

   V₁ = i + 2j
   |V₁| = √2² + 1² = √5
   By drawing velocity diagram
   
   

   α = tan-1			2			= 63.44
   			1

   
   By applying sine rule
   

   		√5	=	V2
   		sin 45		sin 71.57

   
   ∴ V₂ = 3 m/sec

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37. A wheel of radius r rolls without slipping on a horizontal surface shown below. If the velocity of point P is 10 m/s in the horizontal direction, the magnitude of velocity of point Q (in m/s) is _____.
    

1. 1. 20m/s

   
   
   

   2. 19m/s

   
   
   

   3. 21m/s

   
   
   

   4. 10m/s

   
   
   

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1. View Hint View Answer Discuss in Forum

   Vp = r ω = 10 m/s
   Vq = 2 r ω = 2 × 10 = 20 m/s

   Correct Option: A

   Vp = r ω = 10 m/s
   Vq = 2 r ω = 2 × 10 = 20 m/s

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38. A circular object of radius /rolls without slipping on a horizontal level floor with the center having velocity V. The velocity at the point of contact between the object and the floor is

1. 1. zero

   
   
   

   2. V in the direction of motion

   
   
   

   3. V opposite to the direction of motion

   
   
   

   4. V vertically upward from the floor

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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39. A straight rod length L(t), hinged at one end freely extensible at the other end, rotates through an angle θ(t) about the hinge. At time t, L(t) = 1 m, L(t) = 1 m/s, θ(t) = π/4 rad and θ (t) = 1 rad/s. The magnitude of the velocity at the other end of the rod is

1. 1. 1 m/s

   
   
   

   2. √2 m/s

   
   
   

   3. √3 m/s

   
   
   

   4. 2 m/s

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   v = √1² + 1² = √2 m / s
   

   Correct Option: B

   
   v = √1² + 1² = √2 m / s
   

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40. A shell is fired from a cannon. At the instant the shell is just about to leave the barrel, its velocity relative to the barrel is 3 m/s, while the barrel is swinging upwards with a constant angular velocity of 2 rad/s. The magnitude of the absolute velocity of the shell is

1. 1. 3 m/s

   
   
   

   2. 4 m/s

   
   
   

   3. 5 m/s

   
   
   

   4. 7 m/s

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   ωr = 2 × 2 = 4m/sec
   υ_net = √3² + 4² = 5 m / s
   

   Correct Option: C

   
   ωr = 2 × 2 = 4m/sec
   υ_net = √3² + 4² = 5 m / s
   

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