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: (A) (m/√3) (B) (m/2) (C) 2m (D) m

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-2w1tzn5ahn78w9wb.jpg" /> Apply principle of conservation of momentum, Along x- direction, mu=mv1cos45+Mv2cos45 mu=(1/√2)(m v1 + M v2)...(.i.) Along y- direction, 0=mv1sin45-Mv2sin45 0=(m v1 - M v2)(1/√2)...(.ii.) Coefficient of Resolution, e=1 ⇒ (v2 - v1 cos 90/u cos 45)=1 ⇒ (v2/(u)√2)=1 ⇒ u=√2v2...(.iii.) Solving equation (.i.),(.ii.) &(.iii.) , we get M=m

Q. 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 $9 0^{\circ}$ with respect to each other. The mass of unknown particle is:

$\frac{m}{3}$

$\frac{m}{2}$

$2 m$

$m$

Q. 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:

3​m​

2m​

2m

m

Q. 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 $9 0^{\circ}$ with respect to each other. The mass of unknown particle is:

$\frac{m}{3}$

$\frac{m}{2}$

$2 m$

$m$