A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 9 0 ∘ with respect to each othe

Question

A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 9 0 ∘ with respect to each other. The mass of unknown particle is:

TestHub · Accepted Answer

Apply principle of conservation of momentum along $x$ -direction, $m u m u = m v_{1} cos 4 5^{\circ} + M v_{2} cos 4 5^{\circ} = \frac{1}{2} (m v_{1} + M v_{2})$ Along $y$ -direction, $o = m v_{1} sin 4 5^{\circ} - M v_{2} sin 4 5^{\circ} o = (m v_{1} - M v_{2}) \frac{1}{2}$
Coefficient of restution $e = 1$ $= \frac{v _{2} - v _{1} cos 90}{u cos 45}$ ( $∵$ Collision is elastic) $\Rightarrow \frac{v _{2}}{\frac{u}{2}} = 1 \Rightarrow u = 2 v_{2}$ Solving eqs (i), (ii), \& (iii), we get mass of unknown particle, $M = m$

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