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?

$A$ 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:

As shown in the figure,forces of $10^5\,N$ each are applied in opposite directions on the upper and lower faces of a cube of side $10\,cm$,shifting the upper face parallel to itself by $0.5\,cm$. If the side of another cube of the same material is $20\,cm$,then under similar conditions as above,the displacement will be ......... $cm$.

$A$ cube has side length $5$ cm and modulus of rigidity $10^5$ $N$/m$^2$. The displacement produced by a force of $10$ $N$ in the upper face of cube is . . . . . . mm.

Two wires $A$ and $B$ of same length and of same material have radii $r_1$ and $r_2$ respectively. Their one end is fixed with a rigid support and at the other end,an equal twisting couple is applied. Then,the ratio of the angle of twist at the end of $A$ to the angle of twist at the end of $B$ will be ..............

$A$ 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 $8 \times 10^{11} \, N/m^2$).