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A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms–1, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is : (g =10ms–2)
  • a)
    30 m
  • b)
    10 m
  • c)
    40 m
  • d)
    20 m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A piece of wood of mass 0.03 kg is dropped from the top of a 100 m hei...

Time taken for the particles to collide,

Speed of wood just before collision = gt = 10 m/s & speed of bullet just before collision v-gt = 100 – 10 = 90 m/s
Now, conservation of linear momentum just before and after the collision -
–(0.02) (1v) + (0.02) (9v) = (0.05)v
⇒ 150 = 5v
⇒ v = 30 m/s
Max. height reached by body h = v2/2g


∴  Height above tower = 40 m
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A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms–1, from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is : (g =10ms–2)a)30 mb)10 mc)40 md)20 mCorrect answer is option 'C'. Can you explain this answer?
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