Two bodies of mass 1 kg and 3 kg have position vectors $\hat{i}+2 \hat{j}+\hat{k}$ and $-3 \hat{i}-2

Question

Two bodies of mass 1 kg and 3 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\

Professor PC Thomas Classes · Answer

(a): $\vec{r}_{1}=\hat{i}+2 \hat{j}+\hat{k}$ for $M_{1}=1 \mathrm{~kg}$\ $\vec{r}_{2}=-3 \hat{i}-2 \hat{j}+\hat{k}$ for $M_{2}=3 \mathrm{~kg}$\ $r_{\mathrm{C} . \mathrm{M} .}=\frac{\sum m_{i} r_{i}}{\sum m_{i}}$\ $\Rightarrow \quad r_{	ext {C.M. }}=\frac{(1 \hat{i}+2 \hat{j}+1 \hat{k}) 	imes 1+(-3 \hat{i}-2 \hat{j}+\hat{k}) 	imes 3}{4}$\ $\Rightarrow \quad r_{	ext {C.M. }}=\frac{-8 \hat{i}-4 \hat{j}+4 \hat{k}}{4}=-2 \hat{i}-\hat{j}+\hat{k}$.