Two bodies of mass 2g and 10g have position vectors 3i + 2j -u and 3i - j+ 3u respectively. Find the position vector of centre of mass.

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Two bodies of mass 2g and 10g have position vectors $3i+2j-u$ and $3i-j+3u$respectively. Find the position vector of centre of mass.

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$M_1=2g,\, \vec r_1=3\hat i+2\hat j -u$

$M_2=10g,\, \vec r=3\hat i -\hat j+3u$

Position vector of centre of mass = $\frac{M_1r_1+M_2r_2}{M_1+M_2}$

= $\frac{2(3i+2j-u)+10(3i-j+3u)}{10+2}$= $3i-\frac{1}{2}j+\frac{7}{3}u$

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