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Question

Two weight W1andW2 are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with an acceleration g/2. The tension in the string will be:-

A
4W1W2W1+W2
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B
W1W2W1+W2
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C
W1W23(W1+W2)
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D
none of these
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Solution

The correct option is D 4W1W2W1+W2
Letm1=w1g[w=mg]m2=w2g............(1)m2gT=m2(ag)Tm1g=m1(a+g).........(2)m2gm1g=m2am2g+m1a+m1g2m2g=2m1g+a(m1+m2)a=2g(m2m1)(m2+m1)..........(3)byeq.(1),(2)&(3),T=m1g+m1a+m1g=m1(2g+a)=w1g[2g+2g(m2m1m2m1)]=w1[2(m2+m1)2(m2m1)(m2+m1)]=w1⎢ ⎢ ⎢4w2gw2+w1g⎥ ⎥ ⎥=4w1+w2w1+w2


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