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

Question

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, $\frac{V_a-V_b}{V_a+V_b}$, $\frac{\mathrm{m}_{\mathrm{a}}+\mathrm{m}_{\mathrm{b}}}{\mathrm{m}_{\mathrm{a}}}$, 1, $\frac{1}{2}$

MARKS App · Accepted Answer

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

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