A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2 : 2 : 3. The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s each. The velocity of the heavier fragment i $s ____m/s.$
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Question

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2 : 2 : 3. The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s each. The velocity of the heavier fragment i $s ____m/s.$

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G1 Physics · Accepted Answer

The total mass ratio is 2+2+3 = 7. Since the original mass is 14 kg, the three fragment masses are 4 kg, 4 kg and 6 kg. Initial momentum is zero. Choose the velocities of the two equal fragments along negative x and negative y: p⃗₁ = -4×18 î, p⃗₂ = -4×18 ĵ. Let the velocity of the heavier fragment be v⃗₃. Conservation of linear momentum gives p⃗₁ + p⃗₂ + 6v⃗₃ = 0. Therefore, -72î -72ĵ + 6v⃗₃ = 0. Hence, v⃗₃ = 12î + 12ĵ m/s. Its magnitude is |v⃗₃| = √(12²+12²) = 12√2 m/s. Correct option: B.

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2 : 2 : 3. The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s each. The velocity of the heavier fragment i s ____m/s.