Particle A makes a perfectly elastic collision with another particle B at rest. They fly apart in opposite directions with equal speeds. The ratio of their masses `m_A//m_B` is 

Options

A. `1/2`
B. `1/3`
C. `1/4 `
D. `1/(sqrt3)`

Answer

B

Explanation

According to law of conservation of linear momentum, we get
`m_1u_1 + m_2 xx 0 = m_1 v_1 + m_2 (-v_1) = (m_1 - m_2) v_1 " " ….(i)`
`:. (u_1)/(v_1) = (m_1 - m_2)/(m_1) " "……..(ii)`
According to law of conservatoin of kinetic energy, we get
`1/2 m_1 u_1^2 = 1/2 (m_1 + m_2)v_1^2 " "........(iii)`
Divide (iii) by (i) , we get
`u_1 ((m_1 + m_2)v_1)/(m_1 - m_2) " or " (u_1)/(v_1) = (m_1 + m_2)/(m_1 - m_2) " " .....(iv)`
From (ii) and (iv) , we get `(m_1 - m_2)/(m_1) = (m_1 + m_2)/(m_1 - m_2)`
On solving , we get, `(m_1)/(m_2) = 1/3 " or " (m_A)/(m_B) = 1/3`.