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Question

# In the shown pulley-block system, strings are light. Pulleys are massless and smooth and system is released from rest. In 0.6 second, what is the work done by gravity on 20 kg and 10 kg block respectively ? Take [g=10 m/s2]

A
120 J;30 J
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B
30 J;120 J
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C
240 J;60 J
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D
240 J;60 J
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Solution

## The correct option is C 240 J;−60 JUsing constraints, if acceleration of 10 kg is a upwards, acceleration of 20 kg is 2a downwards, FBD for both bodies 2T−10g=10a.....(1)20g−T=40a.......(2) From (1) & (2) 30g=90a a=g3 Displacement of 20 kg block =12at2=12×2g3×0.62=1.2 m Therefore as per the pulley system arrangement Displacement of 10 kg=1.22=0.6 m ∴ Work done on 20 kg block by gravity =mgh=20×10×1.2=240 J Work done on 10 kg block =−mgh2 (moving up) =−10×10×1.22 =−60 J Hence option C is the correct answer

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