A partical of mass `m` moving with velocity `1m//s` collides perfectly elastically with another particle of mass `2m`. If the incident particle is deflected by `90^(circ)`. The heavy mass will make and angle `theta` with the initial direction of `m` equal to:

Options

A. `60^(circ)`
B. `45^(circ)`
C. `15^(circ)`
D. `30^(circ)`

Answer

D

Explanation

Conservation of momentum along incident direction
`m xx 1 = 2m v_(2) cos theta` …..(1)
Conservation of momentum along perpendicular dierction
`m xx 0+2m xx 0 = m v_(1) - 2m v_(2) sin theta`

From energy conservation
`(1)/(2) m xx (1)^(2) = (1)/(2)m v_(1)^(2) + (1)/(2) 2m v_(2)^(2)` .....(3)
From eq. (1). eq. (2) and eq. (3)
We get `theta = 30^(circ)`