The minimum kinetic energy of the meson as a whole system | TestHub

Passage / Comprehension

Meson is composed of two quarks and the interaction between the quarks is complicated. Research of meson can be done by studying the inelastic collisions between the meson and high energy electrons. As the collision is quite complicated, scientists invented a simplified model called ``parton model'' to grasp the main content during collision. In the model, the electron first collides with part of meson (e.g. one of the quarks) elastically. Then the energy and momentum are transferred to the other quark and thus the whole meson during subsequent interaction. This simplified model is described by the following:

An electron of mass M and energy E collides with a quark of mass $m_{1}$ in a meson. The other quark in the meson has mass $m_{2}$ . The quarks are connected by a massless spring of natural length L which is at equilibrium before collision. All movements are on a straight line and neglect the effect of relativity. Find, after collision,

The minimum kinetic energy of the meson as a whole system

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Solution:

After the hit, $v_{1} = \frac{2 M v}{M + m _{1}}$ with $E = \frac{1}{2} M v^{2}$ ; the meson's total momentum is $P = m_{1} v_{1}$ . The meson's KE is minimum when its internal oscillation energy is momentarily zero: $K E_{min} =$ $\frac{P ^{2}}{2 ( m _{1} + m _{2} )}$ .

$K E_{m i n} = \frac{4 M ^{2} m _{1}^{2} v ^{2}}{2 ( M + m _{1} ) ^{2} ( m _{1} + m _{2} )} = \frac{4 M m _{1}^{2} E}{( M + m _{1} ) ^{2} ( m _{1} + m _{2} )} .$

Answer: (A)

Physics - Center of Mass Question with Solution | TestHub

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