The upper end of a wire of diameter $12\,mm$ and length $1\,m$ is clamped and its other end is twisted through an angle of $30^{\circ}$. The angle of shear is $........^{\circ}$.

The dimensions of shear modulus are

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 . . . . . . .

As shown in the figure,forces of $10^5\,N$ each are applied in opposite directions on the upper and lower faces of a cube of side $10\,cm$,shifting the upper face parallel to itself by $0.5\,cm$. If the side of another cube of the same material is $20\,cm$,then under similar conditions as above,the displacement will be ......... $cm$.

Two wires $A$ and $B$ of the same length and of the same material have the respective radii $r_1$ and $r_2$. Their one end is fixed to a rigid support,and at the other end,an equal twisting couple is applied. The ratio of the angle of twist at the end of $A$ to the angle of twist at the end of $B$ will be:

The modulus of rigidity of diamond is: