Work Energy And Power Question 106

Question: A body of mass 50 kg is projected vertically upwards with velocity of 100 m/sec. 5 seconds after this body breaks into 20 kg and 30 kg. If 20 kg piece travels upwards with 150 m/sec, then the velocity of other block will be [RPMT 1999]

Options:

A) 15 m/sec downwards

B) 15 m/sec upwards

C) 51 m/sec downwards

D) 51 m/sec upwards

Show Answer

Answer:

Correct Answer: A

Solution:

Velocity of 50 kg. mass after 5 sec of projection $ v=u-gt $

$ =100-9.8\times 5=51\ m/s $

At this instant momentum of body is in upward direction $ {P _{initial}}=50\times 51=2550\ kg-m/s $

After breaking 20 kg piece travels upwards with 150 m/s let the speed of 30 kg mass is V $ {P _{final}}=20\times 150+30\times V $

By the law of conservation of momentum $ {P _{\text{initial }}}={P _{final}} $
therefore $ 2500=20\times 150+30\times V\Rightarrow V=-15\ m/s $

i.e. it moves in downward direction.



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