A stationary body explodes in to four identical fragments such that three of them fly mutually perpendicular to each other, each with same `KE(E_(0))`. The energy of explosion will be

Answer

6

Explanation

`vec(p _(1)) = mv _(0) hat i`
`vec (p _(2)) = mv _(0) hatj`
`vec ( p _(3)) = mv _(0) hatk`
`vec ( p _(4)) = mvecv`
`0 = vec( p _(1)) + vec ( p _(2)) + vec( p _(3)) + vec( p _(4))`
`vecv =- vec v_(0) ( hati + hatj + hatk)`
`v = v _(0) sqrt3`
Total energy
`= 3 xx (1)/(2) mv _(0) ^(2) + (1)/(2) mv ^(2) = 3 E _(0) + 3 E _(0) = 6 E _(0)`