A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of and coordinates of center of mass of plate is ?. The value of is

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Solution

Q.
A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of $x$ and $y$ coordinates of center of mass of plate is $\frac{n}{9}$ . The value of $n$ is _____. [2024]

Ans.
(15)

$\Rightarrow m_{1} x_{1} + m_{2} x_{2} = m_{3} x_{3}$

$10 x_{1} + 2 (1.5) = 12 (1.5) \Rightarrow x_{1} = 1.5 cm$

$\Rightarrow m_{1} y_{1} + m_{2} y_{2} = m_{3} y_{3}$

$10 y_{1} + 2 (1.5) = 12 \times 1 \Rightarrow y_{1} = 0.9 cm$

$\frac{x_{1}}{y_{1}} = \frac{1.5}{0.9} = \frac{15}{9} \Rightarrow n = 15$

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