\(P Q R\) is a triangular lamina with \(P Q = 18 \mathrm {~cm} , Q R = 24 \mathrm {~cm}\) and \(P R = 30 \mathrm {~cm}\).
Verify that angle \(P Q R\) is a right angle and find the distances of the centre of mass of the lamina from (i) \(P Q\), (ii) \(Q R\).
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The lamina is held in a vertical plane and placed on a line of greatest slope of a rough plane inclined at an angle \(\theta\) to the horizontal, as shown.
Find the largest value of \(\theta\) for which equilibrium will not be broken by toppling.