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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, ac−aB+ac+aA+aA+aB+aB−aA=0 aA+aB+2aC=0 Consider the FBD of different blocks and apply Newton's law seperately, Let tension in string be T mAg−T=mAaA,mBg−T=mBaB,mCg−2T=mCaC ⇒T=6.5 N,aA=g3,aB=g3,aC=−g3

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