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 90 ° with respect to each other. The mass of unknown particle is:

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 90 ° with respect to each other. The mass of unknown particle is:, m 3, m 2, 2 m, m

MARKS App · Accepted Answer

Apply principle of conservation of momentum along x - direction, m u = m v 1 cos ⁡ 45 + M v 2 cos ⁡ 45 m u = 1 2 m v 1 + M v 2 ...(i) along y - direction, o = m v 1 sin ⁡ 45 - M v 2 sin ⁡ 45 o = m v 1 - M v 2 1 2 ...(ii) Coefficient of Resolution ( e) = 1 = v 2 - v 1 cos ⁡ 90 u cos ⁡ 45 ⇒ v 2 u 2 = 1 ⇒ u = 2 v 2 ...(iii) Solving equation (i), (ii) & (iii) we get M = m

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