A 5kg stationary bomb is exploded in three parts having masses in the ratio `1: 1:3`. Parts having same mass move in perpendicular directions with velocity 39m/s, then the velocity of bigger part will be

Options

A. `(10 sqrt2)/(3) m//s`
B. `(10)/(sqrt2) m//s`
C. `13 sqrt2 m//s`
D. `15 sqrt2 m//s`

Answer

C

Explanation

Momentum is conserved in the event of explosion `therefore p_(3)^(2)= p_(1)^(2) + p_(2)^(2)`
Let the mass of the three parts be m, m and 3m
`(3mv_(3))^(2)= (m xx 39)^(2) + (mxx 39)^(2) rArr 39 sqrt2 = 3v_(3), v_(3)= 13 sqrt2 m//s`