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Question

# In the pulley system shown in figure, the movable pulleys A,B and C are of mass 1 kg each. D and E are fixed pulleys. The strings are light and inextensible. Choose the correct alternative (s). (Assume g=9.8 ms−2)

A
Tension in the string is nearly equal to 6.5 N
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B
Acceleration of pulley A is g3 downward
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C
Acceleration of pulley B is g6 upward
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D
Acceleration of pulley C is g3 upward
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Solution

## The correct options are A Tension in the string is nearly equal to 6.5 N B Acceleration of pulley A is g3 downward D Acceleration of pulley C is g3 upward As the string is inextensible, total change in length of the string should be zero. From the figure (yB−yA)+yB+2yA+(yC−yB)+yC=constant Take the second derivative of this equation w.r.t. time to get aA+aB+2aC=0...(1) Here (aA,aB,aC) are accelerations( acting downwards) of A,B,C respectively. Equations of motion for each movable pulley can be written as T+mg−2T=maA T+mg−2T=maB mg−2T=maC Substituting m=1 kg , we get g−T=aA....(2) g−T=aB....(3) g−2T=aC....(4) Substituting (2),(3),(4) in (1) g−T+g−T+2(g−2T)=0 4g−6T=0 T=2g3=6.53 N Substituting T in (2),(3),(4), we get aA=aB=−aC=g3 ⇒ A,B has downward accelration of g3 and C has upward acceleration of g3

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