Q99 / 110 · VITEEE 2022 · Physics

The velocity of a body of rest mass \(m_o\) is \(\frac{\sqrt{3}}{2} c\) (Where \(\mathrm{c}\) is the velocity of light in vacuum). The mass of this body is

  • A
    \(\left(\frac{\sqrt{3}}{2}\right) \mathrm{m}_{\mathrm{o}}\)
  • B
    \(\left(\frac{1}{2}\right) \mathrm{m}_{\mathrm{o}}\)
  • Correct answer
    C
    \(2 \mathrm{~m}_0\)
  • D
    \(\left(\frac{2}{\sqrt{3}}\right) \mathrm{m}_{\mathrm{o}}\)

Solution

\(\mathrm{m}=\frac{\mathrm{m}_{\mathrm{o}}}{\left(1-\frac{\mathrm{v}^2}{\mathrm{c}^2}\right)^{1 / 2}}=\frac{\mathrm{m}_{\mathrm{o}}}{(1-3 / 4)^{1 / 2}}=2 \mathrm{~m}_0\)

Hence, the correct answer is option: 'C'.

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