Shear modulus is zero for

Two wires of the same length and same material have radii $r_1$ and $r_2$. Their one end is fixed,and when an equal torque is applied to the other end,what is the ratio of their angular displacement?

Two slabs with square cross-sections of different materials $(1, 2)$ have equal sides $(l)$ and thicknesses $d_1$ and $d_2$ such that $d_2 = 2d_1$ and $l > d_2$. Considering the 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 modulus of material $1$ is $4 \times 10^9 \ N/m^2$,then the shear modulus of material $2$ is $x \times 10^9 \ N/m^2$,where the value of $x$ is . . . . . . .

$A$ 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,$G = 10^{10} \ N/m^2$)

The modulus of rigidity of diamond is:

$A$ $2 \ m$ long rod of radius $1 \ cm$,which is fixed from one end,is given a twist of $0.8 \ radian$. The shear strain developed (in radian) will be $:-$