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  4. 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 :

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Q. 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 :

JEE MainJEE Main 2022System of Particles and Rotational Motion

Solution:

$\overrightarrow{r_{c o m}}= \frac{m_1 \overrightarrow{r_1}+m_2 \overrightarrow{r_2}}{m_1+m_2}=\frac{1(\hat{ i }+2 \hat{ j }+\hat{ k })+3(-3 \hat{ i }-2 \hat{ j }+\hat{ k })}{1+3} $
$= -2 \hat{ i }-\hat{ j }+\hat{ k }$
$ |2 \hat{ i }-\hat{ j }+\hat{ k }|=\sqrt{(2)^2+(1)^2+(1)^2}=\sqrt{6}$