A bomb in the steady state explodes into three fragments. Two fragments of equal masses move with velocity 15 `ms^(-1)` in mutually perpendicular directions. The mass of the third fragment is equal to three times the mass of each of these two fragments. The magnitude of velocity of third fragment is `ms^(-1)` .

Options

A. 20
B. `10sqrt(2)`
C. `5sqrt(2)`
D. none of these

Answer

C

Explanation

According to law of conservation of momentum initial momentum of bomb = final momentum of bomb
`0=mv_(1) hat( I ) = mv^(2) hat(j ) + 2mv_(3)`
`:. , vec( v )_(3) = (-5) hat(I ) + (-5)hat(j )`
`|vec(v)_(3)| = sqrt(-5)^(2) + (-5)^(2))`
`=sqrt(25 xx 2) = 5 squr(2) m//s`