A particle of mass 4 m explodes into three pieces of masses, m, m and 2 m. The equal masses move along X-axis and Y-axis with velocities 4` ms^(-1)and 6 ms^(-1) ` respectively. The magnitude of the velocity of the heavier mass is

Explanation

`M=4m, u=0, m_(1)=m, m_(2)=m, m_(3)=2m`
`v_(1)=4ms^(-1), v_(2)=6ms^(-1), v_(3)=?`
According to law of conservation of momentum,
`vec(P_(1))+vec(P_(2))+vec(P_(3))=0`
`vec(P_(3))=-(vec(P_(1))+vec(P_(2))),|vec(P_(3))|=|vec(P_(1))+vec(P_(2))|`
`P_(2)=sqrt(P_(1)^(2)+P_(2)^(2)+2P_(1)P_(2)cos theta)`
`P_(1) and P_(2)` are perpendicular to each other
`P_(3)=sqrt(P_(1)^(2)+P_(2)^(2)), m_(3)v_(3)=sqrt((m_(1)v_(1))^(2)+(m_(2)v_(2))^(2))`
`2mv_(3)=sqrt((mxx4)^(2)+(mxx6)^(2))`
`2v_(3)=sqrt(16+36) rArr v_(3)=sqrt(13)ms^(-1)`