Relativistic Mass Exam Question

[Sarah0001]

1.

Homework Equations

E=mc^2
Relativistic mass equation given in the question

The first part of the question:
I understand 200 MeV is the energy lost as it initially moves with 200MeV however is brought to rest and thus this total kinetic energy must have been transferred from the 'two equal parts'
For the worked solution below,

Q : I am confused on how the total energy E=mc^2 = 200 MeV as implied in the work solution.
3. I thought
E_k = mc^2 - m_oc^2

does the worked solution instead mean that
delta theta = m - m_o
and so delta theta = 200MeV/ c^2

The second Part of the question: What speed did the two masses have?

I see the worked solution rearranges the relativistic mass equation to make v the subject, it does this by using the approximation m = m_o as delta m is so small
Q : however I am confused why they plug in 200*10^6 eV for delta m in the 2nd to last line of working shown.

 

[TSny]

If m and m_o refer to the relativistic and rest masses of one of the fragments, then Δm would equal ½ ⋅ 200 Mev/c². But then,
m_o ≈ ½ (2.21 x 10⁵ Mev/c²). If you use these values for Δm and m_o in the expression

then you can check that this gives the same result as the expression given in the solutions:

since the ½ factors cancel.

Note, however, that evaluation does not give

. This is not the correct answer.