The ratio of lengths of two rods $A$ and $B$ of the same material is $1:2$ and the ratio of their radii is $2:1$. What is the ratio of the modulus of rigidity of $A$ and $B$ (in $:1$)?

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

$A$ wire of length $1 \text{ m}$ and radius $2 \text{ mm}$ is vertically clamped. The lower end is twisted through an angle of $45^{\circ}$. The angle of shear is $.....$ (in $^{\circ}$)

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:

Shear modulus is zero for