Question

Two slabs with square cross section of different materials (1, 2) with equal sides (l) and thickness \(d_1\) and \(d_2\) such that \(d_2 = 2d_1\) and \(l>d_2\) . Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is \(\theta _2 = 2 \theta_1\). If the shear moduli of material 1 is \(4 \times 10^9 \ N/m^2\), then shear moduli of material 2 is \(x \times 10^9 \ N/m^2\) , where value of x is ____.

Answer 1

Answer is : (1)

Deformation angle

\(2 \theta _1 = \theta _2\)

\(\Rightarrow 2 \frac{\sigma_1}{\eta_1} = \frac{\sigma_1}{\eta_2}\)

\(\Rightarrow 2 \left(\frac{F}{\ell d_1\eta_1}\right) = \frac{F}{\ell d_2\eta_2}\)

\(\Rightarrow \eta_2 = \frac{\eta_1}{4} = 1 \times 10^9 \Rightarrow x= 1\)