Question

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

• A. $-2\hat{i}+2\hat{k}$
• B. $-2\hat{i}-1\hat{j}+\hat{k}$
• C. $2\hat{i}-\hat{j}-2\hat{k}$
• D. $-\hat{i}+\hat{j}+\hat{k}$

Answer 1

Answer: (B)

$-2\hat{i}-1\hat{j}+\hat{k}$

Given,

Masses are $m_1=1kg{m}_2=3kg$

$Vectors=r_1=2\hat{j}+\hat{i}+\hat{k}$ $r_2=-3\hat{i}-2\hat{j}+\hat{k}$

Position vector of the center of mass

$R=\frac{m_1{r}_1+m_2{r}_2}{m_1+m_2}=\frac{1(2\hat{j}+\hat{i}+\hat{k})+3(-3\hat{i}-2\hat{j}+\hat{k})}{1+3}=\frac{\hat{i}+2\hat{j}+\hat{k}-9\hat{i}-6\hat{j}+3\hat{k}}{4}$

$R=\frac{4(-2\hat{i}-\hat{j}+\hat{k})}{4}=-2\hat{i}-\hat{j}+\hat{k}$