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A disc of radius r is removed from the disc of radius R then which of the following are true

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The minimum shift in center of mass is zero

The minimum shift in center of mass cannot be greater than $\frac{r^{2}}{R+r}$

Center of mass must lie where mass exists

The shift in center of mass is $\frac{r^{2}}{R+r}$

answer is A, B.

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Detailed Solution

Shift in the centre mass will be minimum, when the cut is concentric.

Maximum shift will be when it is adjacent to the edge

$∆ x_{cm} = \frac{m_{1} r_{1} + m_{2} r_{2}}{m_{1} + m_{2}}$

$= \frac{λ π R^{2} (0) - λ π r^{2} (R - r)}{λ π R^{2} - λ π r^{2}} = \frac{r^{2}}{R + r}$

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