Question

A body of mass $ 2\, kg $ moving with a velocity $ \left(\hat{i}+2\hat{j}-3\hat{k}\right) \,m/s $ collides with another body of mass $ 3\, kg $ moving with a velocity $ \left(2\hat{i}+\hat{j}+\hat{k}\right)\,m/s $ . If they stick together, the velocity in $ m/s $ of the composite body is

• A. $ \frac{1}{5}\left(8\hat{i}+7\hat{j}-3\hat{k}\right) $
• B. $ \frac{1}{5}\left(-4\hat{i}+\hat{j}-3\hat{k}\right) $
• C. $ \frac{1}{5}\left(5\hat{i}+\hat{j}-\hat{k}\right) $
• D. $ \frac{1}{5}\left(-4\hat{i}+8\hat{j}-3\hat{k}\right) $

Answer 1

Answer: (A)

We know that $p =m v$
So, $ p _{1} =2(\hat{ i }+2 \hat{ j }-3 \hat{ k }) kg \,m / s$
$=(2 \hat{ i }+4 \hat{ j }-6 \hat{ k }) kg\, m / s $
and $p _{2} =3(2 \hat{ i }+\hat{ j }+\hat{ k }) m / s$
$=(6 \hat{ i }+3 \hat{ j }+3 \hat{ k }) kg m / s $
Resultant momentum is
$p = p _{1}+ p _{2}$
$=(2 \hat{ i }+4 \hat{ j }-6 \hat{ k })+(6 \hat{ i }+3 \hat{ j }+3 \hat{ k })$
$=(8 \hat{ i }+7 \hat{ j }-3 \hat{ k }) kg m / s$
Total mass $(m)=2+3=5\, kg$
Therefore, the velocity of body is
$v =\frac{p}{m}=\frac{1}{5}(8 \hat{ i }+7 \hat{ j }-3 \hat{ k }) \,m / s $
$=\frac{1}{5}(8 \hat{ i }+7 \hat{ j }-3 \hat{ k })\, m / s $