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:

Step-by-step solution

Apply principle of conservation of momentum along x -direction, aligned m u &=m v₁ 45^ +M v₂ 45^ m u &= 1 2 (m v₁+M v₂ ) aligned Along y -direction, aligned &o=m v₁ 45^ -M v₂ 45^ &o= (m v₁-M v₂ ) 1 2 aligned Coefficient of restution e=1 = v₂-v₁ 90 u 45 ( Collision is elastic) aligned & v₂ u 2 =1 & u= 2 v₂ aligned Solving eqs (i), (ii), & (iii), we get mass of unknown particle, M=m