Question

A particle of rest mass $m_0$ moves with a speed $\frac{C}{2}$ its total energy and kinetic energy are:

• A. $\frac{\sqrt{3}}{2}{m}_0{C}^2;\frac{\sqrt{3}}{2}{m}_{0}C$
• B. $\frac{2}{\sqrt{3}}{m}_0{C}^2;\frac{0.25}{\sqrt{3}}{m}_0{C}^2$
• C. $\frac{2}{\sqrt{3}}{m}_0{C}^2;\frac{0.27}{\sqrt{3}}{m}_0{C}^2$
• D. None of these

Answer 1

The correct option is C $\frac{2}{\sqrt{3}}{m}_0{C}^2;\frac{0.27}{\sqrt{3}}{m}_0{C}^2$

$E=\frac{m{c}^2}{\sqrt{1-(\frac{v}{c}{)}^2}}$ at $v=\frac{c}{2}$

$E=\frac{m_0{c}^2}{\sqrt{1-\left(\frac{1}{4}\right)}}=\frac{2m_0{c}^2}{\sqrt{3}}$

$K.E=E-m{c}^2$

$=\frac{2m_0{c}^2}{\sqrt{3}}-m_0{c}^2=\frac{(2-\sqrt{3})}{\sqrt{3}}{m}_0{c}^2$

$=\frac{0.27m_0{c}^2}{\sqrt{3}}$