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?

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:

$A$ 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 modulus of rigidity of diamond is:

$A$ rubber cube of side $5 \ cm$ has one face fixed while a tangential force $1800 \ N$ is applied on its opposite face. If the modulus of rigidity of rubber is $2.4 \times 10^6 \ N \ m^{-2}$,then the lateral displacement of the strained face is $......$ . (in $mm$)

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