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Question

In the pulley system shown in the 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. Find tension in the string.
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Solution

Since, all strings are connected to each other, it will have some tension at all point, let it be T.
Considering the acceleration of pulley, A,B and C is a1,a2 and a3 downward.
according to constrain equation,
T.a=0
2Ta3T.a2Ta1=0
2a3+a2+a1=0(1)
Applying Newton''s laws on each block,
102T=a3(2)
10T=a2(3)
10T=a1(4)
From equation (2) and (3)
T=a3a2
T=a2a3(5)
putting it in
10a2+a3=a2
2a2=10+a3(6)
Solving (2) and (4), we get,

a1=a2=103,a3=103

T=203Newton

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