Particle A makes a head on elastic collision with another stationary particle B. They fly apart in opposite directions with equal speeds. The mass ratio will be

Options

A. `(1)/(2)`
B. `(1)/(2)`
C. `(1)/(4)`
D. `(1)/(sqrt(3))`

Answer

B

Explanation

Here` m_(1)=m_(A), m_(2)=m_(B), u_(1)=u, u_(2)=0`,
`upsilon_(1)=upsilon, upsilon_(2)=0 upsilon `
Applying principle of conservation of linear momentum
`m_(1)u+0=m_(1)upsilon+m_(2)(- upsilon)=(m_(1)-m_(2))upsilon ...(i)`
Applying principle of conservation of K.E.
`(1)/(2) m_(1)u^(2)=(1)/(2)(m_(1)+m_(2))upsilon^(2) ...(ii)`
Dividing `(ii)` and `(i)`, we get
`u=((m_(1)+m_(2))upsilon)/(m_(1)-m_(2))`or`(u)/(upsilon)=(m_(1)+m_(2))/(m_(1)-m_(2)) ...(iii)`
From `(i), (u)/(upsilon)=(m_(1)-m_(2))/(m_(1))`
`:. ` from `(iii), (m_(1)+m_(2))/(m_(1)-m_(2))=(m_(1)-m_(2))/(m_(1))`
On solving , we get
`(m_(1))/(m_(2))=(1)/(3) i.e. (m_(A))/(m_(B))=(1)/(3)`