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 ${90}^o$ with respect to each other. The mass of unknown particle is:

• A. $\frac{m}{2}$
• B. $m$
• C. $\frac{m}{\sqrt{3}}$
• D. $2m$

Answer 1

The correct option is B $m$

Applying principle of conservation of momentum along x-direction

$mu=m{v}_1\cos 45+M{v}_2\cos 45$

$mu=\frac{1}{\sqrt{2}}(m{v}_1+M{v}_2)....\left(1\right)$

Along y-direction

$0=m{v}_1\sin 45-M{v}_2\sin 45$

$m{v}_1=M{v}_2.....\left(2\right)$

Coefficient of Restitution $e=\frac{v_2-v_1\cos 90}{u\cos 45}=1$ (For elastic collision, e=1)

$\frac{v_2}{\frac{u}{\sqrt{2}}}=1$

$v_2=\frac{u}{sqrt2}.......\left(3\right)$

Solving (1), (2) and (3) we get,

$M=m$

Hence, mass of unknown particle is same as mass of proton.