A body of mass `1kg` initially at rest explodes and breaks into three parts of masses in the ration ` 1: 2: 3.` If the two pieces of equal masses fly off perpendicular to each other with a speed of `30m//s` The speed of third piece will be .

Options

A. `10sqrt2m//s`
B. `20sqrt2m//s`
C. `5sqrt2m//s`
D. `40sqrt2m//s`

Answer

a

Explanation

Here, total mass `= 1kg`
`m_(1) : m_(2) : m_(3) = 1: 1: 3`
`:. M_(1) = m_(2) = (1)/(1+1+3) = 0.2kg`
`m_(3) = 1 - 0.4 = 0.6 kg`
`upsilon_(1) = upsilon_(2) = 30m//s`
`p_(1) = p_(2) = 0.2 xx 30 = 6kg m//s`
As `p_(1), p_(2)` are perpendicular to each other so according to law of conservation of linear mo- mentum `p_(3)` should be the resultat of `p_(1)` and `p_(2)`
`:. p_(3) = sqrt( p_(1)^(2) + _(2)^(2)) =sqrt((6)^(2) + (6)^(2)) = 6sqrt2kgm//s`
`p_(3) = m_(3) upsilon_(3) :. upsilon_(3) = (p_(3))/(m_(3)) = (6sqrt2)/(0.6) = 10sqrt2 m//s` .