TS EAMCET · Physics · Center of Mass Momentum and Collision
A circular plate of radius \(r\) is removed from a uniform circular plate \(P\) of radius \(4 r\) to form a hole. If the distance between the centre of the hole formed and the centre of the plate \(P\) is \(2 r\), then the distance of the centre of mass of the remaining portion from the centre of the plate \(P\) is
- A \(\frac{r}{3}\)
- B \(\frac{r}{15}\)
- C \(\frac{2 r}{15}\)
- D \(2 r\)
Answer & Solution
Correct Answer
(C) \(\frac{2 r}{15}\)
Step-by-step Solution
Detailed explanation
Cut area, \(A_C=\pi r^2 \propto l\) Remaining area, \(A_R=\pi(4 r)^2-\pi r^2=15 \pi r^2 \propto 15\) Now, \(A_C X_C=A_R X_R\) \(1 \times 2 \mathrm{r}=15 \mathrm{X}_{\mathrm{R}} \therefore \mathrm{X}_{\mathrm{R}}=\frac{2 \mathrm{r}}{15}\)
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