A particle of mass $3m$ moves in the lab frame with speed $v$ close to the

speed of light and hits another particle with mass $m$ which is at rest in the

lab frame. As a result of the collision both particles disappear and two new

particles of mass $2\mathrm{.}5m$ each are created.

What is the minimum velocity $v_{\text{m}\text{i}\text{n}}$ required for the first particle so this

process will be possible?

a$.v_{\text{m}\text{i}\text{n}}=0\mathrm{.}81c$

b$.v_{\text{m}\text{i}\text{n}}=0\mathrm{.}96c$

c$.$ This process is not possible because there is not enough energy to

create such new two particles.

d$.$ The process is impossible since the final total mass $(5m)$ is larger

than the initial total mass $(4m).$

e$.v_{\text{m}\text{i}\text{n}}=0\mathrm{.}92c$

f$.$ There is no energy conservation in this collision, so $v_{\text{m}\text{i}\text{n}}$ is not well

defined in this case.