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

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 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 $........^{\circ}$.

$A$ force $F$ of the same magnitude is applied tangentially on the upper and lower faces of a cube in opposite directions. The side of the cube is $L$. The upper face of the cube shifts parallel to itself by a distance $x_{1}$. If another cube of the same material but with side $2L$ is subjected to the same condition,then the displacement of the top layer is:

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

$A$ 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 $\text{ GPa}$)