Steel ruptures when a shear stress of $3.5 \times 10^8 \, N \, m^{-2}$ is applied. The force needed to punch a $1 \, cm$ diameter hole in a steel sheet $0.3 \, cm$ thick is nearly:

$A$ wire of length $1 \text{ m}$ and radius $2 \text{ mm}$ is vertically clamped. The lower end is twisted through an angle of $45^{\circ}$. The angle of shear is $.....$ (in $^{\circ}$)

The modulus of rigidity of diamond 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 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?

$A$ 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 $....... \mu m$.