Question 247: Centre of Mass and Rotational Motion

Question

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 ________.

Accepted Answer

$$\begin{array}{ll}
x_{\mathrm{cm}}=1.5 & \
M_{+}=6 \sigma & y_{+}=1 \
M_{-}=-\sigma & y_{-}=1.5
\end{array}$$
$$\begin{aligned}
& y_{\mathrm{cm}}=\frac{6 \sigma 	imes 1+(-\sigma) 	imes 1.5}{6 \sigma-\sigma} \
& =\frac{6-1.5}{5}=\frac{4.5}{5}=0.9 \
& \frac{x}{y}=\frac{1.5}{0.9}=\frac{15}{9}
\end{aligned}$$

Centre of Mass and Rotational Motion

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 ________.

Integer / Numeric Answer Type