A rectangular block of size 10,cm times 8,cm | vedclass

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(C) The modulus of rigidity $\eta$ is defined as the ratio of shearing stress to shearing strain:$\eta = \frac{F/A}{x/L}$where $F$ is the tangential f

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Maximum in $Q$ position

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(C) The modulus of rigidity $\eta$ is defined as the ratio of shearing stress to shearing strain:$\eta = \frac{F/A}{x/L}$where $F$ is the tangential force,$A$ is the area of the face on which the force is applied,$x$ is the lateral displacement,and $L$ is the height of the block perpendicular to the force.Rearranging for displacement $x$:$x = \frac{F \cdot L}{\eta \cdot A}$Since $\eta$ and $F$ are constant for all cases,the displacement $x$ is proportional to the ratio of height to area: $x \propto \frac{L}{A}$.Calculating $L/A$ for each case:For position $P$: $L = 5\,cm$,$A = 10 	imes 8 = 80\,cm^2$. So,$L/A = 5/80 = 0.0625\,cm^{-1}$.For position $Q$: $L = 10\,cm$,$A = 8 	imes 5 = 40\,cm^2$. So,$L/A = 10/40 = 0.25\,cm^{-1}$.For position $R$: $L = 8\,cm$,$A = 10 	imes 5 = 50\,cm^2$. So,$L/A = 8/50 = 0.16\,cm^{-1}$.Comparing the values,the ratio $L/A$ is maximum in position $Q$. Therefore,the displacement is maximum in position $Q$.

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