31. A spring scale indicates a tension T in the right hand cable of the pulley system shown in Neglecting the mass of the pulleys and ignoring friction between the cable and pulley the mass m is
    
    

1. 1. 2T/g
      

   
   
   

   2. T(1 + e^4π)/g
      

   
   
   

   3. 4T/g
      

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   ∑ F_V = 0
   4T = mg
   

   or m =	4T
   	g

   Correct Option: C

   
   ∑ F_V = 0
   4T = mg
   

   or m =	4T
   	g

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32. An elevator (lift) consists of the elevator cage and a counter weight, of mass m Chain each. The cage and the counter weight are connected by chain that passes over a Cage pulley. The pulley is coupled Counter weight to a motor. It is desired that the elevator should have a maximum stopping time of seconds from a peak speed v. If the inertias of the pulley and the chain are neglected, the minimum power that the motor must have is
    

1. 1. 	1	mv²
      	2

   
   
   

   2. 	mv²
      	2t

   
   
   

   3. 	mv²
      	t

   
   
   

   4. 	2mv²
      	t

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Power = dW / dt (rate of doing work or rate of change of K.E. energy of the system)
   Initial Kinetic energy of the system
   

   =		1	= mv² +	1	mv² = mv²
   		2		2

   
   Final Kinetic energy = 0
   Time duration it occurs = t
   

   ⇒ Power =	mv²
   	t

   
   

   Correct Option: C

   Power = dW / dt (rate of doing work or rate of change of K.E. energy of the system)
   Initial Kinetic energy of the system
   

   =		1	= mv² +	1	mv² = mv²
   		2		2

   
   Final Kinetic energy = 0
   Time duration it occurs = t
   

   ⇒ Power =	mv²
   	t

   
   

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33. A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t = 0. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 m/s2 and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of

1. 1. 1

   
   
   

   2. 2

   
   
   

   3. 4

   
   
   

   4. ∞

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   (1) → t =?
   v = u + at
   0 = 4 – 10t
   

   t =	4	= 0.4s
   	10

   
   (2) → t' =?
   u' = 0.8 × u = 0.8 × 4 = 3.2 m/s
   v' = u' + at'
   0 = 3.2 – 10t'
   

   t' =	3.2	= 0.32s
   	10

   
   (3) → t'' =?
   u'' = 0.8 u' = 0.8 × 3.2 = 2.56 m/s
   v'' = u'' + at''
   0 = 2.56 – 10t''
   t'' = 0.256s
   So, t, t', t'' are forming a GP series
   So, total time = 2(t + t' + t'' +.... 0)
   = 2[0.4 + 0.32 + 0.256 + ....0] = 2 × 2 = 4 seconds

   Correct Option: C

   
   (1) → t =?
   v = u + at
   0 = 4 – 10t
   

   t =	4	= 0.4s
   	10

   
   (2) → t' =?
   u' = 0.8 × u = 0.8 × 4 = 3.2 m/s
   v' = u' + at'
   0 = 3.2 – 10t'
   

   t' =	3.2	= 0.32s
   	10

   
   (3) → t'' =?
   u'' = 0.8 u' = 0.8 × 3.2 = 2.56 m/s
   v'' = u'' + at''
   0 = 2.56 – 10t''
   t'' = 0.256s
   So, t, t', t'' are forming a GP series
   So, total time = 2(t + t' + t'' +.... 0)
   = 2[0.4 + 0.32 + 0.256 + ....0] = 2 × 2 = 4 seconds

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34. The following figure shows the velocity time plot for a particle traveling along a straight line. The distance covered by the particle from t = 0 to t = 5s is _______m.
    

1. 1. 10

   
   
   

   2. 9

   
   
   

   3. 11

   
   
   

   4. 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   Distance = Velocity × Time
   Distance from t = 0 to t = 5s
   = Area under the curve from t = 0 to t = 5
   

   =		1	× 1 × 1 + 1 × 1 +	1	× 1 × 3 + 1 × 1 +	1	× 2 × 2 + 2 × 2
   		2		2		2

   
   

   =		1	+ 1 +	3	+	1	+ 2 + 4 = 4 + 2 + 1 + 1 + 2 = 10
   		2		2		1

   
   

   Correct Option: A

   Distance = Velocity × Time
   Distance from t = 0 to t = 5s
   = Area under the curve from t = 0 to t = 5
   

   =		1	× 1 × 1 + 1 × 1 +	1	× 1 × 3 + 1 × 1 +	1	× 2 × 2 + 2 × 2
   		2		2		2

   
   

   =		1	+ 1 +	3	+	1	+ 2 + 4 = 4 + 2 + 1 + 1 + 2 = 10
   		2		2		1

   
   

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35. 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 toP

   
   
   

   4. V_QP has only one component perpendicular to PQ

   
   
   

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1. View Hint View Answer Discuss in Forum

   

   Correct Option: D

   

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