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A body of mass `1kg` initially at rest explodes and breaks into threee fragments of masses in the ration breaks into three fragments of masses in the ration `1: 1: 3`. The two pieces of equal masses fly off perpendicular to each other with a speed of `30m//s` each What is the velocity of heavier fragments ? . |
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Answer» Correct Answer - `10 sqrt2 m//s` . Here, `m = 1kg` `m_(1) : m_(2) : m_(3) = 1 : 1: 3` `:. M_(1) = (1)/(5)kg, m_(2) = (1)/(5)kg, m_(3) =(3)/(5)kg` `upsilon_(1) = upsilon_(2) = 30 m//s, upsilon_(3) =` ? `p_(1) = p_(2) = m_(1) upsilon_(1) = m_(2) upsilon_(2)` `= (1)/(5) xx 30 = 6 kg m//s` As these two pieces fly off perpendicular to each other their resultant momentum `sqrt(p_(1)^(2) + p_(2)^(2)) = sqrt(6^(2) + 6^(2)) = 6sqrt2kgm//s` As the body was initially at rest therefore from the principle of conservation of linear momentum `p_(3) =m_(3) upsilon_(3) =6sqrt2 kg m//s` `upsilon_(3) = (6sqrt2)/(m_(3))= (6sqrt2)/(3//5) = 10 sqrt2 m//s` . |
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