(i) Define the rest mass of a particle.

(ii) The rest mass of a particle is said to be an invariant quantity. State, with reference to special relativity, what is meant by the term invariant.

In a thought experiment, two particles X and Y, each of rest mass 380 MeVc^–2, are approaching each other head on.

The speed of X and of Y is 0.60 c relative to a laboratory.

(i) Calculate the momentum of X in the frame of reference in which Y is at rest.

(ii) As a result of the collision a single particle Z is formed. Determine the rest mass of Z. The gamma factor for a speed of 0.60 c is 1.25.

(i) the mass of an object in its rest frame / the mass as measured by an observer at rest with respect to the body;

(ii) a quantity that is the same for all observers/reference frames;

(i) speed of X relative to Y is \(\left( {\frac{{0.60{\rm{c}} - \left( { - 0.60{\rm{c}}} \right)}}{{1 + {{0.60}^2}}}} \right) = 0.882{\rm{c}}\);
gamma factor at this speed is \(\gamma  = \frac{1}{{\sqrt {1 - {{0.882}^2}} }} = 2.12\);
momentum is then p=γmv= 2.12×380×0.882c=710MeVc⁻¹;
Award [3] for a bald correct answer between 700MeVc⁻¹ and 713MeVc⁻¹ due to rounding.

(ii) \(M{c^2} = 2 \times \gamma m{c^2} = 2 \times \frac{5}{4} \times 380\);
⇒M=950MeVc⁻²;
Award [2] for a bald correct answer.