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a stationary body explodes into 4 identical fragments such that 3 of them fly off mutually perpendicular to each orher.,each with K.E. E.the energy released in explosion will be???

a stationary body explodes into 4 identical fragments such that 3 of them fly off mutually perpendicular to each orher.,each with K.E. E.the energy released in explosion will be???

Grade:11

1 Answers

Sangharakshit Kadam
11 Points
3 years ago
Let the three equal mass fragments move along x, y, z direction with velocity vₒ (each have same k.e = E = ½mvₒ²) . conservation of momentum: before = after => 0 = mv̂ + m[vₒî + vₒĵ + vₒk̂] => v̂ = ivth fragment`s velocity = - [vₒî + vₒĵ + vₒk̂] ---------------------> (i) energy of explosion = k.e(f) - k.e(i) = k.e(f) - 0 = ½m(√3vₒ)² + 3(½mvₒ²) = 6½mvₒ² = 6E

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