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:

• A. $-2\hat{i}-\hat{j}+\hat{k}$
• B. $2\hat{i}-\hat{j}-2\hat{k}$
• C. $-\hat{i}+\hat{j}+\hat{k}$
• D. $-2\hat{i}+\hat{k}$

Answer 1

Answer: (A)

$-2\hat{i}-\hat{j}+\hat{k}$

Answer 2

$\vec{ R }_{ cm }=\frac{ m _{1} \vec{ r }_{1}+ m _{2} \vec{ r }_{2}}{ m _{1}+ m _{2}}=-2 \hat{ i }-\hat{ j }+\hat{ k }$