Answer
a) $B\lt D\lt C\lt A$.
b) $A\lt D\lt B=C$
c) $A\lt D\lt C\lt B$
Work Step by Step
(a) We know that $E_{\circ}=m_{\circ}c^2$. This equation shows that the rest energy of the particle is directly proportional to its rest mass $m_{\circ}$. Therefore, we can conclude that $B\lt D\lt C\lt A$.
(b) We know that
$K=Total\space energy -rest\space energy$
For particle A
$K_A=6E-6E=0$
For particle B
$K_B=4E-2E=2E$
For particle C
$K_C=6E-4E=2E$
For particle D
$K_D=4E-3E=1E$
Thus, $A\lt D\lt B=C$
(c)
We know that the particle which has maximum $\frac{E}{E_{\circ}}$ value, has maximum speed.
For particle A
$\frac{E}{E_{\circ}}=\frac{6E}{6E}=1$
For particle B
$\frac{E}{E_{\circ}}=\frac{4E}{2E}=2$
For particle C
$\frac{E}{E_{\circ}}=\frac{6E}{4E}=1.5$
For particle D
$\frac{E}{E_{\circ}}=\frac{4E}{3E}=1.33$
Thus, $A\lt D\lt C\lt B$
