Question

An object flying in air with velocity $\left(20\hat{i}+25\hat{j}-12\hat{k}\right)$ suddenly breaks in two pieces whose masses are in the ratio $1:5$. The smaller mass flies off with a velocity $\left(100\hat{i}+35\hat{j}+8\hat{k}\right)$. The velocity of the larger piece will be :

• A. $4\hat{i}+23\hat{j}-16\hat{k}$
• B. $-100\hat{i}+35\hat{j}-8\hat{k}$
• C. $20\hat{i}+15\hat{j}-80\hat{k}$
• D. $-20\hat{i}+15\hat{j}-80\hat{k}$

Answer 1

Answer: (A)

Conservation of linear momentum,
$m{\vec{v}}_0=\frac{m}{6}{\vec{v}}_1+\frac{5m}{6}{\vec{v}}_2$
$\Rightarrow m(20\hat{i}+25\hat{j}-12\hat{k})$
$=\frac{m}{6}(100\hat{i}+35\hat{j}+8\hat{k})+\frac{5m}{6}{\vec{v}}_2$
$\Rightarrow {\vec{v}}_2=4\hat{i}+23\hat{j}-16\hat{k}$