🎴 Flashcard Mode
Collisions in one dimension - class-XI
Card1 / 82
Mastered0
Review0
QuestionClick to flip
A particle of mass $1\ g$ moving with a velocity $\vec {v _{1}} = 3\hat {i} - 2\hat {j} ms^{-1}$ experiences a perfectly in elastic collision with another particle of mass $2\ g$ and velocity $\vec {v _{2}} = 4\hat {j} - 6\hat {k} ms^{-1}$. The velocity of the particle is:
AnswerClick to flip back
A
$4.6\ ms^{-1}$
💡 Explanation:
From conservation of momentum
$m _{1}\vec {v _{1}} + m _{2}\vec {v _{2}} = (m _{1} + m _{2})\vec {v}$
$1\times (3\hat {i} - 2\hat {j}) + 2\times (4\hat {j} - 6\hat {k}) = (1 + 2)\vec {v}$
$\Rightarrow 3\hat {i} + 6\hat {j} - 12\hat {k} = 3\vec {v} $
$\Rightarrow \vec {v} = \hat {i} + 2\hat {j} - 4\hat {k}$
$v = |\vec {v}| = \sqrt {1 + 4 + 16} = 4.6\ ms^{-1}$.