0Q. A body of mass 5 kg, initially at rest, explodes and breaks into three fragments of masses in the ratio 1: 1 : 3. The two fragments of equal masses fly off perpendicular to each other, each with a velocity of 21 ms–1. The velocity of the heavier fragment is
(a) 6.5ms–1 (b) 7ms–1 (c) 9.87 ms–1 (d) 11.5 ms–1
Answer (c): Since 5 kg body explodes into three fragments of masses in the ratio 1: 1 : 3, hence masses of the three fragments will be 1 kg, 1 kg and 3 kg, respectively. The magnitude of the resultant momentum of two fragments each of mass 1 kg, moving with velocity 21 m s–1 in
the perpendicular direction is 21 2 kg m s–1.
According to law of conservation of linear momentum,
3 × v = 21 2 or v = 21 2 / 3 = 7 2 = 9.87 m s–1
