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A particle with rest mass M_0 , splits up into two identical fragments which fly apart in opposite directions at speeds of 0.90c. Find the rest mass of each fragment.

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Solution :Before decaying the particle is at rest and its energy is `epsilon_0=M_(0)c^2`. Since it decays into two identical FRAGMENTS their TOTAL energy MUST be `epsilon=2mc^2=(2m_0c^2)/(sqrt(1-beta^2))` where `m_0` is the rest MASS of a fragmentand `u =betac`is its velocity. It follows from the law of conservationof energy that`(2m_0c^2)/(sqrt(1-beta^2))=M_0c^2`whence the rest mass of a fragment is
`m_0=1/2M_0sqrt(1-beta^2)`
Substituting the speed we OBTAIN the rest mass of the fragment.


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