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

Options

A. `4 sqrt2m// s` at an angle of `45^@` from each body
B. `24 sqrt2m//s` at an angle of `135^@` from each body
C. `6 sqrt2m//s` at `135^@` from each body
D. `4 sqrt2m// s` at `135^@` from each body

Answer

D

Explanation

`m_1 v_1 hati +m_2 v_2 hati = m_3v_3`
`implies m xx 12 hati + m xx 12 hatj = 3mv_3`
`implies (12sqrt2)/3 = v_3 impliesv_3 =4sqrt2`