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

Options

A. `13sqrt(2)` m/s
B. `(10)/(sqrt(2))` m/s
C. `15sqrt(2)` m/s
D. `(15)/(sqrt(2))` m/s

Answer

a

Explanation

Here, mass of 3 parts wil be 1 kg , 1 kg and 3 kg.
Applying conservation law of momentum
`|p^2|=sqrt(p_1^2+p_2^2)`
`(3xxV)^2=(1xx39)^2+(1xx39)^2`
`V^2=1/9xx(39)^2(1+1)=((39)^2)/(9)xx2`
`V=1/3xx39sqrt2=13sqrt2 ms^(-1)`