$A$ rectangular metallic block of dimensions $40 \text{ mm} \times 20 \text{ mm}$ when pulled with a tension of $50 \text{ kN}$ undergoes only elastic deformation. The strain in the block is (The shear modulus of the material of the block is $40 \times 10^9 \text{ Nm}^{-2}$)

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

$A$ uniform wire of length $L$ and radius $r$ is twisted by an angle $\alpha$. If the modulus of rigidity of the wire is $\eta$,then the elastic potential energy stored in the wire is .........

$A$ steel plate of face area $1 \, cm^2$ and thickness $4 \, cm$ is fixed rigidly at the lower surface. $A$ tangential force $F = 10 \, kN$ is applied on the upper surface as shown in the figure. The lateral displacement $x$ of the upper surface with respect to the lower surface is .............. $m$ (Modulus of rigidity for steel is $8 \times 10^{11} \, N/m^2$).

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

$A$ rod of length $l$ and radius $r$ is joined to a rod of length $l/2$ and radius $r/2$ of the same material. The free end of the small rod is fixed to a rigid base,and the free end of the larger rod is given a twist of $\theta^\circ$. The twist angle at the joint will be: