Question

A body of mass 2 kg moving with a velocity $(\hat{i}+2\hat{j}-3\hat{k})m{s}^{-1}$ collides with another body of mass 3 kg moving with a velocity $(2\hat{i}+\hat{j}+\hat{k})$ in $m{s}^{-1}$. If they stick together, the velocity in $m{s}^{-1}$ of the composite body is

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

Answer 1

The correct option is A $\frac{1}{5}(8\hat{i}+7\hat{j}-3\hat{k})$

$p_1=2kg(\hat{i}+2\hat{j}-3\hat{k})m{s}^{-1}=(2\hat{i}+4\hat{j}-6\hat{k})kgm{s}^{-1}{p}_2=3kg(2\hat{i}+\hat{j}+\hat{k})m{s}^{-1}=(6\hat{i}+3\hat{j}+3\hat{k})kgm{s}^{-1}$
Resultant momentum is
$p=p_1+p_2$
=$(2\hat{i}+4\hat{j}-6\hat{k})+(6\hat{i}+3\hat{j}+3\hat{k})$
=$(8\hat{i}+7\hat{j}-3\hat{k})kgm{s}^{-1}$
Total mass (m) = 2 + 3 = 5 kg. Therefore, the velocity of composite body is
$v=\frac{p}{m}=\frac{1}{5}(8\hat{i}+7\hat{j}-3\hat{k})m{s}^{-1}$
Hence the correct choice is (a).