Two bodies of mass $1 \mathrm{~kg}$ and $3 \mathrm{~kg}$ 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 :
Solution
<p>$${\overline r _{com}} = {{{m_1}{{\overline r }_1} + {m_2}{{\overline r }_2}} \over {{m_1} + {m_2}}}$$</p>
<p>$= {{(1 - 9)\widehat i + (2 - 6)\widehat j + (1 + 3)\widehat k} \over 4}$</p>
<p>$= {{ - 8\widehat i - 4\widehat j + 4\widehat k} \over 4}$</p>
<p>${\overline r _{com}} = - 2\widehat i - \widehat j + \widehat k$</p>
<p>$\left| {\overline r } \right| = \sqrt {4 + 1 + 1} = \sqrt 6$</p>
<p>$\left| {\widehat i + 2\widehat j + \widehat k} \right| = \sqrt 6$</p>
About this question
Subject: Physics · Chapter: Rotational Motion · Topic: Centre of Mass
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