The dimensions of shear modulus are

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 $:1$)?

When a spiral spring is stretched by suspending a load from it,the strain produced is called . . . . . . strain.

$A$ force $F$ of the same magnitude is applied tangentially on the upper and lower faces of a cube in opposite directions. The side of the cube is $L$. The upper face of the cube shifts parallel to itself by a distance $x_{1}$. If another cube of the same material but with side $2L$ is subjected to the same condition,then the displacement of the top layer is:

$A$ square aluminium (shear modulus is $25 \times 10^{9} \, N m^{-2}$) slab of side $60 \, cm$ and thickness $15 \, cm$ is subjected to a shearing force (on its narrow face) of $18.0 \times 10^{4} \, N$. The lower edge is riveted to the floor. The displacement of the upper edge is $....... \mu m$.

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 . . . . . . .