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QJEEM24Ph099b: JEE Main 2024 Physics - Class 11 JEEM24Ph099b Solution: A uniform thin metal plate of mass with dimensions is shown.…

A uniform thin metal plate of mass 10 kg10 \mathrm{~kg} with dimensions is shown. The ratio of x\mathrm{x} and y coordinates of center of mass of plate in n9\frac{n}{9} . The value of nn is ________.

JEE Main 2024 (Online) 8th April Morning Shift Physics - Center of Mass and Collision Question 6 English

Step-by-Step Verified Solution

xcm=1.5amp;M+=6σamp;y+=1M−=−σamp;y−=1.5\begin{array}{ll}x_{\mathrm{cm}}=1.5 & \\M_{+}=6 \sigma & y_{+}=1 \\M_{-}=-\sigma & y_{-}=1.5\end{array}

amp;ycm=6σ×1+(−σ)×1.56σ−σamp;=6−1.55=4.55=0.9amp;xy=1.50.9=159\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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