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Q.

A uniform triangular plate of triangular area $1 m^{2}$ , base length 60 cm and thickness 10 mm (prism like shape) is lying vertically on a smooth ground as shown in figure. The maximum value of $\cot θ$ for which it does not topple is n, find 100n?

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answer is 36.

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Detailed Solution

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Just to prevent from toppling, mg must pass through toppling point.
$x_{C M} = 60 = \frac{0 + 60 + x}{3} \Rightarrow x = 120 c m$
Area $= \frac{1}{2} \times \frac{60}{100} \times y = 1 \Rightarrow y = \frac{10}{3} m$
$\cot θ = \frac{x}{y} = \frac{120}{100 \times 10} \times 3 = 0.36$

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