The upper end of a wire of radius $4 \, mm$ and length $100 \, cm$ is clamped and its other end is twisted through an angle of $60^o$. The angle of shear is .......... $^o$.

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

Two slabs with square cross-sections of different materials $(1, 2)$ have equal sides $(l)$ and thicknesses $d_1$ and $d_2$ such that $d_2 = 2d_1$ and $l > d_2$. Considering the lower edges of these slabs are fixed to the floor,we apply equal shearing force on the narrow faces. The angle of deformation is $\theta_2 = 2\theta_1$. If the shear modulus of material $1$ is $4 \times 10^9 \ N/m^2$,then the shear modulus of material $2$ is $x \times 10^9 \ N/m^2$,where the value of $x$ 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 $mm$)

Given below are two statements: One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A)$: The stretching of a spring is determined by the shear modulus of the material of the spring.
Reason $(R)$: $A$ coil spring of copper has more tensile strength than a steel spring of same dimensions.
In the light of the above statements,choose the most appropriate answer from the options given below:

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