Two masses ' $\mathrm{m}_{\mathrm{a}}$ ' and ' $\mathrm{m}_{\mathrm{b}}$ ' moving with velocities '…

Two masses ' $\mathrm{m}_{\mathrm{a}}$ ' and ' $\mathrm{m}_{\mathrm{b}}$ ' moving with velocities ' $\mathrm{v}_{\mathrm{a}}$ ' and ' $\mathrm{v}_{\mathrm{b}}$ ' opposite directions collide elastically. Alter the collision ' $\mathrm{m}_{\mathrm{a}}$ ' and ' $\mathrm{m}_{\mathrm{b}}$ ' move with velocities and ' $\mathrm{v}_{\mathrm{b}}$ ' and ' $\mathrm{v}_{\mathrm{a}}$ ' respectively, then the ratio $\mathrm{m}_{\mathrm{a}}: \mathrm{m}_{\mathrm{b}}$ is
  1. $\frac{v_a+v_b}{v_a-v_b}$
  2. $\frac{1}{2}$
  3. 1
  4. $\frac{v_a-v_b}{v_a+v_b}$

Solution

When two bodies of equal masses collide elastically, they exchange their velocities. Since the two masses are exchanging their velocities, their masses must be equal. Hence, $\frac{\mathrm{m}_{\mathrm{a}}}{\mathrm{m}_{\mathrm{b}}}=1$

Asked in: MHT CET 2021 (20 Sep Shift 1)

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