Two particles, of masses M and 2M, moving as shown, with speeds of `10m//s` and `5m//s`, collide elastically at the origin.After the collision, they move along the indicated directions with speeds `v_1` and `v_2` , respectively.The values of `v_1` and `v_2` are nearly :

Options

A. 6.5 m/s and 6.3 m/s
B. 3.2 m/s and 6.3 m/s
C. 3.2 m/s and 12.3 m/s
D. 6.5 m/s and 3.2 m/s

Answer

A

Explanation

From conservation of momentum
Along x-direction:
`M(10) cos 30^@ + (2M) (5) cos 45^@ = (2M).v_1 cos 30^@ + M.v_2 cos 45^@`
`implies sqrt(3)v_1 + (v_2)/(sqrt2) = 5sqrt(3) + 5sqrt(2) " "….(i)`
Along y-direction:
`(2M) xx(5) sin 45^@ - M (10) sin 30^@ = (2M) v_1 sin 30^@ - Mv_2 sin 45^@`
`implies v_1 - (v_2)/(sqrt2) = 5sqrt(2) - 5" ".....(ii)`
Solving (i) & (ii)
`v_1 = 6.5 m//s , v_2 = 6.3 m//s` .