Question

A body of mass 1 kg initially at rest explodes and
breaks into three fragments of masses in the ratio
1:1: 3. The two pieces of equal masses fly off
perpendicular to each other with speed v each.
What is the momentum of heavier fragment?​

Answer 1

The Sage

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 * 30 m/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.