Question

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

Answer 1

Correct Answer - 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^(@)`