A body, initially at rest, explodes into two pieces of mass 2m and 3m respectively, having a total kinetic energy E. What is the KE of the piece of mass 2M after the explosion?
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Answer:
initial momentum = 0
By linear conservation of momentum, final momentum = 0.
Hence,
(2m) V1 + (3m) V2 = 0
V2 = -2/3 V1
Total kinetic energy = E
½ (2m)(V1)² + ½ (3m)(V2)² = E
½ (2m)(V1)² + ½ (3m)(4/9)(V1)² = E
m(v1)² = 3E/5
so, ½ (2m) (v1)² = 3E/5
KE of the piece of mass 2M after the explosion is 3E/5
