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Question

An inextensible massless string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in N) is


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Solution

Method I:

Tension in string
[2m1m2m1+m2]g
⎢ ⎢ ⎢2×100g×200g100g+200g⎥ ⎥ ⎥g
⎢ ⎢ ⎢ ⎢2×100×200g2(100+200)g⎥ ⎥ ⎥ ⎥×g
2×100×200300=4003=133.33N
Method II:

Assume weight starts moving with acceleration 'a', while tension in string is T1
Free body diagram of block having 10 N weight,

T1100=100ag...(i)
Free body diagram of block having 200 N

200T1=200ag...(ii)
Dividing equation (i) with equation (ii)
T1100200T1=100200
2T1200=200T1
3T1=400
Tension in string,
T1=4003=133.33N

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