JEE MAIN - Physics (2024 - 8th April Morning Shift - No. 26)
A uniform thin metal plate of mass $$10 \mathrm{~kg}$$ with dimensions is shown. The ratio of $$\mathrm{x}$$ and y coordinates of center of mass of plate in $$\frac{n}{9}$$. The value of $$n$$ is ________.
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Answer
15
Explanation
$$\begin{array}{ll} x_{\mathrm{cm}}=1.5 & \\ M_{+}=6 \sigma & y_{+}=1 \\ M_{-}=-\sigma & y_{-}=1.5 \end{array}$$
$$\begin{aligned} & y_{\mathrm{cm}}=\frac{6 \sigma \times 1+(-\sigma) \times 1.5}{6 \sigma-\sigma} \\ & =\frac{6-1.5}{5}=\frac{4.5}{5}=0.9 \\ & \frac{x}{y}=\frac{1.5}{0.9}=\frac{15}{9} \end{aligned}$$
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