Shear Modulus & Poisson's Ratio

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

Match List I with List II:

Choose the correct answer from the options given below:

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of $10^{5}\text{ N}$ 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 moduli, $G = 10^{10}\text{ N/m}^2$)

Two slabs with square cross section of different materials $(1, 2)$ with equal sides $(l)$ and thickness $d_1$ and $d_2$ such that $d_2 = 2d_1$ and $l > d_2$. Considering 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 moduli of material 1 is $4 \times 10^{9}\text{ N/m}^2$, then shear moduli of material 2 is $x \times 10^{9}\text{ N/m}^2$, where value of $x$ is ________.

Choose the correct relationship between Poisson ratio $(\sigma)$, bulk modulus (K) and modulus of rigidity $(\eta)$ of a given solid object:

A square aluminum (shear modulus is $25 \times 10^{9}\text{ Nm}^{-2}$) slab of side $60\text{ cm}$ and thickness $15\text{ cm}$ is subjected to a shearing force (on its narrow face) of $18.0 \times 10^{4}\text{ N}$. The lower edge is riveted to the floor. The displacement of the upper edge is ____________ $\mu$m.

If Y, K and $\eta$ are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

For homogeneous isotropic material, which one of the following cannot be the value of Poisson's ratio?

As shown in the figure, forces of 105 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:

In materials like aluminium and copper, the correct order of magnitude of various elastic moduli is:

Steel ruptures when a shear of 3.5 $\times$ 108 N m−2 is applied. The force needed to punch a 1 cm diameter hole in a steel sheet 0.3 cm thick is nearly:

A uniform wire (Young's modulus $2 \times 10^{11}$ Nm $^{-2}$) is subjected to longitudinal tensile stress of $5 \times 10^{7}$ Nm$^{-2}$. If the overall volume change in the wire is 0.02%, the fractional decrease in the radius of the wire is close to: