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^(@)`
B. `45^(@)`
C. `15^(@)`
D. `30^(@)`

Answer

D

Explanation

From coservation of momentum along incident direction
`mxx1=2mv_(2)costheta`…….i
From conservation of momentum along perpendicular direction,
`mxx0+2mxx0=mv_(1)-2mv_(2)sintheta`
`implies v_(1)=2v_(20sintheta`…………ii

From energy conservartion
`1/2mxx(1)^(2)=1/2mv_(1)^(2)+1/22mv_(2)^(2)`.......iii
From eqn i, ii and iii we get `theta=306^(@)`