# Particle decay: Relativistic or classical?

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1. Nov 3, 2016

### Isomorphism

This question was asked in an competitive exam in India.

The relevant equations are momentum conservation in the classical sense and the 4 momentum conservation.

My attempt: Classical momentum conservation would seem inaccurate since the kinetic energies are high. However, a straightforward application of it yields option (a). I think it is wrong since we end up with more energy than we started with. Initial energy is 3GJ, but final energy is 10 GJ since C has 8GJ of energy.

I wanted to know how to solve it using special relativity. It looks like information about the masses is missing.(I know that I cannot use conservation of masses.) So I am wondering whether it is possible to solve this problem with relativistic corrections and whether the answer still remains 30 degrees.

Thanks,

Last edited: Nov 3, 2016
2. Nov 3, 2016

### PeroK

It's got nothing to do with Relativity. The piece that went off at right angles should have $1 GJ$ not $2 GJ$.

3. Nov 3, 2016

### Isomorphism

How did you know that it is a classical momentum problem apriori?

The energies of the two pieces are 8GJ and 2GJ.

I have updated my original post.

4. Nov 3, 2016

### PeroK

If it was a SR problem, it would have said "relativistic velocity", not "high velocity".

5. Nov 3, 2016

### vela

Staff Emeritus
1 GJ might sound like a lot, but if you calculate the equivalent amount of mass, you find $m = \frac{10^9}{(3\times10^8)^2}= 1.1\times 10^{-8}\text{ kg}.$ The mass of the missile is many orders of magnitude above that.

6. Nov 3, 2016

### PeroK

Or, if the missile had a mass of $1 kg$ then its velocity would be less than $8 \times 10^4 m/s$

7. Nov 3, 2016

### Isomorphism

Thanks for that clarification.

If it is classical, how has the total energy increased?

8. Nov 3, 2016

### PeroK

That would be a mistake in the question, as pointed out in post #2.