Two bodies of mass $1 \mathrm{~kg}$ and $3 \mathrm{~kg}$ have position vectors $\hat{\mathrm{i}}+2…

Two bodies of mass $1 \mathrm{~kg}$ and $3 \mathrm{~kg}$ have position vectors $\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $-3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$, respectively. The centre of mass of this system has a position vector :
  1. $-\hat{i}+\hat{j}+\hat{k}$
  2. $-2 \hat{i}+2 \hat{k}$
  3. $-2 \hat{i}-\hat{j}+\hat{k}$
  4. $2 \hat{i}-\hat{j}-2 \hat{k}$

Solution

$\quad \overrightarrow{\mathrm{R}}_{\mathrm{cm}}=\frac{\mathrm{m}_1 \overrightarrow{\mathrm{r}}_1+\mathrm{m}_2 \overrightarrow{\mathrm{r}}_2}{\mathrm{~m}_1+\mathrm{m}_2}=-2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$

Asked in: NEET 2009 (Mains)

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