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A body of mass explodes at rest break up...

A body of mass explodes at rest break up into three parts.If two parts having equal masses fly off perpendicularly to each other with a velocity of `18 m//s`, then calculate the velocilty of the third part which has a mass `3` times the mass of each part.

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Initially the body is at rest. Initial linear momentum of the body is zero. Let due to explosion the body break up into three parts. There is no external force acting on the body. Hence linear momentum just after collision also be zero.

Let total mass of the body be `5 cm`, hence the masses of the broken parts will be `m, m` and `3m` respectively.
`vecp_("initial")=0`
Linear momentum just after explosion
`vecp_("final")=vecp_(1)+vecp_(2)+vecp_(3)=mv_(1)hati+mv_(1)hatj+vecp_(3)`
As `vecp_("initial")=vecp_("final")implies|vecp_(3)|=sqrt(2)mv_(1)implies3mv=sqrt(2)mv_(1)`
`v=(sqrt(2)v_(1))/3=(sqrt(2)xx18)/3=6sqrt(2)ms^(-1)`
`implies 6sqrt(2)ms^(-1)` at an angle `135^(@)` from the either ball.
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