The ratio of lengths of two rods $A$ and $B$ of the same material is $1:2$ and the ratio of their radii is $2:1$. What is the ratio of the modulus of rigidity of $A$ and $B$ (in $:1$)?

$A$ rectangular metallic block of dimensions $40 \text{ mm} \times 20 \text{ mm}$ when pulled with a tension of $50 \text{ kN}$ undergoes only elastic deformation. The strain in the block is (The shear modulus of the material of the block is $40 \times 10^9 \text{ Nm}^{-2}$)

$A$ slab of side $50 \text{ cm}$ and thickness $10 \text{ cm}$ is subjected to a shearing force of $10^5 \text{ N}$ on its narrow edge. If the lower edge is riveted to the floor and the upper edge is displaced by $0.2 \text{ mm}$, then the shear modulus of the material of the slab is: (in $\text{ GPa}$)

The edge of an aluminium cube is $10\; cm$ long. One face of the cube is firmly fixed to a vertical wall. $A$ mass of $100\; kg$ is then attached to the opposite face of the cube. The shear modulus of aluminium is $25\; GPa$. What is the vertical deflection of this face?

$A$ cylindrical rod of length $1 \ m$ and radius $4 \ cm$ is mounted vertically. It is subjected to a shear force of $10^5 \ N$ at the top. Considering infinitesimally small displacement in the upper edge,the angular displacement $\theta$ of the rod axis from its original position would be: (Shear modulus,$G = 10^{10} \ N/m^2$)

Shear modulus is zero for