First slide

Methods to locate centre of mass

Question

From the circular disc of radius 4R two small disc of radius R are cut off. The centre of mass of the new structure will be:

Moderate

A

$\hat{i} \frac{R}{5} + \hat{j} \frac{R}{5}$
B

$- \hat{i} \frac{R}{5} + \hat{j} \frac{R}{5}$
C

$\frac{- 3 R}{14} (\hat{i} + \hat{j})$
D

None of these

Solution

If mass of removed disc is m then mass of big disc will be 16 m.
$x_{cm} = \frac{16 m (0) - m (0) - m (3 R)}{16 m - m - m} = - \frac{3}{14} R$
Because of symmetry we can say $y_{cm}$ will also have same magnitude
$y_{cm} = - \frac{3}{14} R$
${\vec{r}}_{cm} = - \frac{3}{14} R (\hat{i} + \hat{j})$

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