Question

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

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

Answer 1

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

We know that $p=mv$

So, $p_1=2(\hat{i}+2\hat{j}-3\hat{k})kgm/s$

$=(2\hat{i}+4\hat{j}-6\hat{k})kgm/s$

and $p_2=3(2\hat{i}+\hat{j}+\hat{k})kgm/s$

$=(6\hat{i}+3\hat{j}+3\hat{k})kgm/s$

Resultant momentum is

$p=p_1+p_2$

$=(2\hat{i}+4\hat{j}-6\hat{k})+(6\hat{i}+3\hat{j}+3\hat{k})$

$=(8\hat{i}+7\hat{j}-3\hat{k})kgm/s$

Total mass(m) $=2+3=5kg$

Therefore, the velocity of body is

$v=\frac{p}{m}=\frac{1}{5}(8\hat{i}+7\hat{j}-3\hat{k})m/s$

$=\frac{1}{5}(8\hat{i}+7\hat{j}-3\hat{k})m/s$