Question

A body of mass $3kg$ moving with a velocity $(2\hat{i}+3\hat{j}+2\hat{k})m/s$ collides with another body of mass $4kg$ with a velocity $(3\hat{i}+2\hat{j}-3\hat{k})m/s$. The two bodies stick together after collision. The velocity of the composite body is

• A. $\frac{1}{7}(4\hat{i}+6\hat{j}-3\hat{k})$
• B. $\frac{1}{7}(18\hat{i}+17\hat{j}-6\hat{k})$
• C. $\frac{1}{7}(6\hat{i}+4\hat{j}-6\hat{k})$
• D. $\frac{1}{7}(9\hat{i}+8\hat{j}-6\hat{k})$

Answer 1

Answer: (B)

$\frac{1}{7}(18\hat{i}+17\hat{j}-6\hat{k})$

Given : $m_1=3kg$ $\overrightarrow{u_1}=$ $2\hat{i}+3\hat{j}+2\hat{k}$ $m_2=4kg$ $\overrightarrow{u_2}=3\hat{i}+2\hat{j}-3\hat{k}$
Let the velocity of composite body be $\overrightarrow{V}$.
Using conservation of momentum :
$(m_1+m_2)\overrightarrow{V}=m_1\overrightarrow{u_1}+m_2\overrightarrow{u_2}$
$(3+4)\overrightarrow{V}=3$$(2\hat{i}+3\hat{j}+2\hat{k})+4$$(3\hat{i}+2\hat{j}-3\hat{k})$
$7\overrightarrow{V}=$ $18\widehat{i+17\hat{j}-6\hat{k}}$
$⟹\overrightarrow{V}=\frac{1}{7}$$\left(18\widehat{i+17\hat{j}-6\hat{k}}\right)$