| A homogeneous circular plate of radius r has a circular hole as shown below. |
 |
| Coordinates of centre of mass of plate with respect to given origin is |
A) \[(0,0)\]
B) \[\left( -\frac{r}{2},0 \right)\]
C) \[\left( -\frac{r}{6},0 \right)\]
D) \[\left( -\frac{r}{6},\frac{r}{6} \right)\]
Correct Answer: C
Solution :
| The x-coordinate of complete disc |
| Is \[{{X}_{CM}}=\frac{{{m}_{1}}{{x}_{1}}+{{m}_{2}}{{x}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] |
| Treating removed mass \[{{m}_{2}}\]as negative mass, we have |
| \[0=\frac{\frac{3}{4}m\cdot {{x}_{0}}+\frac{m}{4}\cdot \frac{r}{2}}{\frac{3}{4}m+\frac{m}{4}}\]\[\Rightarrow \]\[{{x}_{0}}=\frac{-r}{6}\] |
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