6. A body of mass 1 kg initially at rest, explodes andbreaks into thre

1.	6. A body of mass 1 kg initially at rest, explodes andbreaks into three fragments of masses in the ratio1 :1: 3. The two pieces of equal mass fly-offperpendicular to each other with a speed of 30 m/seach. What is velocity of heavier fragment?(1) 5 m/s(3) 5v2 m/s(4) 10v2 m/s(2) 10 m/s
Answer» Masses of fragments: 1/5 * 1kg, 1/5* 1kg, 3/5 * 1kg ie., 0.2 kg, 0.2 kg, 0.6 kg Linear momentum of theirs: 0.2 * 30m/s = 6 kg-m/s, 6 kg-m/s, 0.6 * v kg-m/s The vector sum of the first two : 6√2 kg-m/s as they two linear momenta are perpendicular. This will be in North East direction, if the two pieces fly off in North and East directions respectively. So linear momentum of the large piece is in the direction of South West direction as Linear momentum of all three pieces is 0 (as before explosion). Velocity of the third piece = 6√2 kg-m/s / 0.6 kg = 10√2 m/s in South West dir.

6. A body of mass 1 kg initially at rest, explodes andbreaks into three fragments of masses in the ratio1 :1: 3. The two pieces of equal mass fly-offperpendicular to each other with a speed of 30 m/seach. What is velocity of heavier fragment?(1) 5 m/s(3) 5v2 m/s(4) 10v2 m/s(2) 10 m/s

Answer»

Masses of fragments: 1/5 * 1kg, 1/5* 1kg, 3/5 * 1kg ie., 0.2 kg, 0.2 kg, 0.6 kg

Linear momentum of theirs: 0.2 * 30m/s = 6 kg-m/s, 6 kg-m/s, 0.6 * v kg-m/s

The vector sum of the first two : 6√2 kg-m/s as they two linear momenta are perpendicular. This will be in North East direction, if the two pieces fly off in North and East directions respectively.

So linear momentum of the large piece is in the direction of South West direction as Linear momentum of all three pieces is 0 (as before explosion).

Velocity of the third piece = 6√2 kg-m/s / 0.6 kg = 10√2 m/s in South West dir.

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