Q110 / 110 · VITEEE 2022 · Physics

Two masses \(\mathrm{m}_{\mathrm{a}}\) and \(\mathrm{m}_{\mathrm{b}}\) moving with velocities \(\mathrm{v}_{\mathrm{a}}\) and \(\mathrm{v}_{\mathrm{b}}\) in opposite direction collide elastically and after the collision \(\mathrm{m}_{\mathrm{a}}\) and \(\mathrm{m}_{\mathrm{b}}\) move with velocities \(\mathrm{V}_{\mathrm{b}}\) and \(\mathrm{V}_{\mathrm{a}}\) respectively. Then the ratio \(\mathrm{m}_{\mathrm{a}} / \mathrm{m}_{\mathrm{b}}\) is

  • A
    \(\frac{V_a-V_b}{V_a+V_b}\)
  • B
    \(\frac{\mathrm{m}_{\mathrm{a}}+\mathrm{m}_{\mathrm{b}}}{\mathrm{m}_{\mathrm{a}}}\)
  • Correct answer
    C
    1
  • D
    \(\frac{1}{2}\)

Solution

As velocities are exchanged on perfectly elastic collision, therefore masses of two objects must be equal. \(\therefore \frac{\mathrm{m}_{\mathrm{a}}}{\mathrm{m}_{\mathrm{b}}}=1 \text { or } \mathrm{m}_{\mathrm{a}}=\mathrm{m}_{\mathrm{b}} \text {. }\)

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

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