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