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 magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector.

• A. $\hat i+2\hat j+\hat k$
• B. $−3\hat i−2 \hat j+\hat k$
• C. $−2\hat j+2\hat k$
• D. $−2\hat i−\hat j+2\hat k$

Answer 1

Answer: (A)

$\hat i+2\hat j+\hat k$

Answer 2

$\bar r_{com}=\frac {m_1\bar r_1+m_2\bar r_2}{ m_1+m_2}$

$\bar r_{com}=\frac {(1−9)\hat i+(2−6)\hat j+(1+3)\hat k}{4}$

$\bar r_{com}=\frac {-8\hat i-4\hat j+4\hat k}{4}$
$\bar r_{com}=−2\hat i−\hat j+\hat k$
$|\bar r|=\sqrt {4+1+1}$
$|\bar r|=\sqrt 6$
$|\hat i+2\hat j+\hat k|=\sqrt 6$

So, the correct option is (A): $\hat i+2\hat j+\hat k$