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Question

Consider a body at rest in the L-frame, which explodes into two fragments of masses m1 and m2.
Calculate energies of the fragments of the body
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Solution

Since the body is initially at rest, its total momentum is zero. As a result of the explosion, the two fragments will separate in opposite directions with momenta p1 and p2 such that p1+p2=0; magnitude of momentum will be same, i.e., p1=p2.
On substituting,
Ek=p212m1+p222m2=12(1m1+1m2)p1
Ek=0
In Eq. (iv) of kinematics of reaction, we get
12(1m1+1m2)p21=Q
On rearranging this equation, we get
p1=(2m1m2m1+m2Q)1/2=(2μ12Q)1/2
where μ12 is the reduced mass of the system. The kinetic energies of the fragments are p212m1 and p222m2 with p1=p2. Hence,
Ek,1=p212m1=m1Qm1+m2 and Ek,2=p222m2=m2Qm1+m2

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