A nucleus moving with velocity `bar(v)` emits an `alpha`-particle. Let the velocities of the `alpha`-particle and the remaining nucleus be `bar(v)_(1)` and `bar(v)_(2)` and their masses be `m_(1)` and `(m_2)` then,

Options

A. All velocity vectors `vecv,vecv_(1)` and `vecv_(2)` must be parallel.
B. `vecv` must be parallel to `(vecv_(1)+vecv_(2))`
C. `vecv` must be parallel to `(m_(1)vecv_(1)+m_(2)vecv_(2))`
D. None of these

Answer

C

Explanation

Before emitting `vecp_(i)=(m_(1)+m_(2))vecv` in horizontal direction
`alpha`- particle

After emitting `vecp_(f)=m_(1)vecv_(1)+m_(2)vecv_(2)`
in horizontal direction
by conservation of L.M.
`vecp_(i)=vecp_(f)`
`(m_(1)+m_(2))vecv=m_(1)vecv_(1)+m_(2)vecv_(1)`
Thus `vecv` must be parallel to
`(m_(1)vecv_(1)+m_(2)vecv_(2))`
as `vecv=(m_(1)vecv_(1)+m_(2)vecv_(2))/((m_(1)+m_(2)))`