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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). All pulleys are frictionless.

A
Tension in the string is 6.5 N
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B
Acceleration of pulley A is g/3 downward
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C
Acceleration of pulley B is g/6 upward
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D
Acceleration of pulley C is g/3 upward
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Solution

The correct options are
A Tension in the string is 6.5 N
B Acceleration of pulley A is g/3 downward
D Acceleration of pulley C is g/3 upward
For finding the constraint realtion between blocks A, B and C, let's assume the acceleration of blocks are aA,aB and aC and in downward direction.
Apply intercept method for l1,l2,....l6 in diagram we get,
acaB+ac+aA+aA+aB+aBaA=0
aA+aB+2aC=0

Consider the FBD of different blocks and apply Newton's law seperately,
Let tension in string be T

mAgT=mAaA,mBgT=mBaB,mCg2T=mCaC
T=6.5 N,aA=g3,aB=g3,aC=g3

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