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 20kg and 10kg block respectively ? Take [g=10m/s2]
A
120J;30J
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B
30J;120J
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C
240J;−60J
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D
−240J;60J
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Solution
The correct option is C240J;−60J Using constraints, if acceleration of 10kg is a upwards, acceleration of 20kg is 2a downwards,
FBD for both bodies
2T−10g=10a.....(1)20g−T=40a.......(2)
From (1) & (2)
30g=90a a=g3
Displacement of 20kg block
=12at2=12×2g3×0.62=1.2m
Therefore as per the pulley system arrangement Displacement of 10kg=1.22=0.6m
∴ Work done on 20kg block by gravity =mgh=20×10×1.2=240J
Work done on 10kg block =−mgh2 (moving up) =−10×10×1.22 =−60J