The force required to punch a square hole of side $2\,cm$ in a steel sheet of thickness $2\,mm$ is (given: shearing stress of steel sheet $= 3.5 \times 10^8\,N/m^2$)

The strain energy stored in a body of volume $V$ due to shear strain $\phi$ is (shear modulus is $\eta$ ).

$A$ horizontal aluminium rod of diameter $4 \text{ cm}$ projects $6 \text{ cm}$ from a wall. An object of mass $400 \pi \text{ kg}$ is suspended from the end of the rod. The shearing modulus of aluminium is $3.0 \times 10^{10} \text{ N/m}^2$. The vertical deflection of the end of the rod is (given $g = 10 \text{ m/s}^2$): (in $\text{ mm}$)

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

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?

The units of modulus of rigidity are