Q107 / 200 · NEET 2009 (Screening) · Physics
Two bodies of mass $1 \mathrm{~kg}$ and $3 \mathrm{~kg}$ have position vectors $\hat{i}+2 \hat{j}+\hat{k}$ and $-3 \hat{i}-2 \hat{j}+\hat{k}$, respectively. The centre of mass of this system has a position vector
- A$-2 \hat{i}+2 \hat{k}$
- Correct answerB$-2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$
- C$2 \hat{i}-\hat{j}-2 \hat{k}$
- D$-\hat{i}+\hat{j}+\hat{k}$
Solution
The position vector of centre of mass
$$
\begin{aligned}
\vec{r} & =\frac{m_1 \overrightarrow{r_1}+m_2 \vec{r}_2}{m_1+m_2} \\
& =\frac{1(\hat{i}+2 \hat{j}+\hat{k})+3(-3 \hat{i}-2 \hat{j}+\hat{k})}{1+3} \\
& =\frac{1}{4}(-8 \hat{i}-4 \hat{j}+4 \hat{k}) \\
& =-2 \hat{i}-\hat{j}+\hat{k}
\end{aligned}
$$
The centre of mass changes its position only under the translatory motion. There is no effect of rotatory motion on centre of mass of the body.
Hence, the correct answer is option: 'B'.