First slide

Centre of mass(com)

Question

Eight solid uniform cubes of edge l are stacked together to form a single cube with center O. One cube is removed from this system. Distance of the center of mass of remaining 7 cubes from O is

Moderate

A

$\frac{7 \sqrt{3} l}{16}$
B

$\frac{\sqrt{3} l}{16}$
C

$\frac{\sqrt{3} l}{14}$
D

$z e r o$

Solution

Let the position of C.M. of remaining structure from O is $\vec{r}$
$\begin{array}{l} \vec{r} = \frac{8 m \times 0 - m (\frac{l}{2} \hat{i} + \frac{l}{2} \hat{j} + \frac{l}{2} \hat{k})}{7 m} = \frac{- l (\hat{i} + \hat{j} + \hat{k})}{14} \\ \Rightarrow | \vec{r} | = \frac{\sqrt{3} l}{14} \end{array}$

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