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A body at rest breaks up into 3 parts. I...

A body at rest breaks up into `3` parts. If `2` parts having equal masses fly off perpendicularly each after with a velocity of `12 m//s` when the velocity of the third part which has `3 times` mass of each part is

A

`4 sqrt(2) m//s` at an angle of `45^(@)` from each body

B

`24 sqrt(2) m//s` at an angle of `135^(@)` from each body

C

`4 sqrt(2) m//s` at `90^(@)` from each body

D

`4sqrt(2)m//s` at `135^(@)` from each body

Text Solution

Verified by Experts

The correct Answer is:
D

By the momentum conservation
`x : 5 m xx 0 = m xx 12 + 3 m v cos hteta rArr v cos theta = - 4`
`y : 5m xx 0 = m xx 12 + 3m v sin theta rArr v sin theta = - 4`
The third piece will move
` v = 4 sqrt(2) m//s , theta = 45^(@)`


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