A particle of mass m, moving along the X-axis collides with a stationary particle of mass `m_2` and deviates by an angle `30^@ ` to the X-axis as shown in the figure. If the percentage change in kinetic energy of the combined system of these two particles reduces by 50%, then the ratio of the masses `m_2/m_1` is

Options

A. 8
B. 6
C. `8/7`
D. `1/6`

Answer

A

Explanation

Momentum is conserved in both x and y direction separately
`rArr m_1 u = m_2 v_2 cos 30^@ " " ….(i)`
and `m_1 v_1 = m_2 v_2 sin 30^@` ….(ii)
Also , loss of K.E = 50%
` rArr 50 = (1/2 m_1u^2 - 1/2 m_1v_1^2 - 1/2 m_2v_2^2)/(1/2 m_1u^2) " " ....(iii)`
solving eqs . (i) , (ii) and (iii) , we get
`m_2/m_1= 8`