A body of mass 1 kg at rest explodes into three fragments of masses in the ratio 1 : 1 : 3 . The two pieces of equal mass fly in mutually perpendicular directions with a speed of `30 m//s` each . What is the velocity of the heavier fragment ?

A body of mass 1 kg at rest explodes into three fragments of masses in

1.	A body of mass 1 kg at rest explodes into three fragments of masses in the ratio 1 : 1 : 3 . The two pieces of equal mass fly in mutually perpendicular directions with a speed of `30 m//s` each . What is the velocity of the heavier fragment ?
Answer» As total mass is 1 kg and fragments masses are in the ratio 1 : 1 : 3 , therefore , ` m_(1) = m_(2) = (1)/(5) kg and m_(3) = (3)/(5) kg ` also, ` upsilon_(1) = upsilon_(2) = 30 m//s , upsilon_(3) = ` ? According to the principal of conservation of linear momentum ` vec(p_(1))+ vec(p_(2))+ vec(p_(3))=0 ` ` vec(p_(3))+ vec(p_(1))+ vec(p_(2))=sqrt(p_(1)^(2)+p_(2)^(2))` ` m_(3) upsilon =m_(1) sqrt(upsilon_(2)^(1)+ upsilon_(2)^(2))=(1)/(5)sqrt(30^(2)+30^(2)` ` (3)/(5)upsilon_(3) =6 sqrt2 ` ` upsilon_(3) = (6 sqrt2xx5 )/(5)=10 sqrt2 = 14 . 14 m//s ` .

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A body of mass 1 kg at rest explodes into three fragments of masses in the ratio 1 : 1 : 3 . The two pieces of equal mass fly in mutually perpendicular directions with a speed of `30 m//s` each . What is the velocity of the heavier fragment ?

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