Centre of Mass 1 Question 16
16. A circular plate of uniform thickness has a diameter of $56 cm$. A circular portion of diameter $42 cm$ is removed from one edge of the plate as shown in figure.
Find the position of the centre of mass of the remaining portion.
(1980)
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Answer:
Correct Answer: 16. $9 cm$ from centre of bigger circle (leftwards)
Solution:
- Suppose $r _1$ be the distance of centre of mass of the remaining portion from centre of the bigger circle, then
$$ \begin{aligned} A _1 r _1 & =A _2 r _2 \\ r _1 & =\frac{A _2}{A _1} r _2 \\ & =\frac{\pi(42)^{2}}{\pi\left[(56)^{2}-(42)^{2}\right]} \times 7=9 cm \end{aligned} $$
