Grade 11 : Physics - Solids (Set 3)

A steel wire of original length 2 m and cross-sectional area $1\text{ mm}^2$ is stretched by a force of 100 N. If the extension produced is 1 mm, what is the Young's modulus of the wire material?

A metal rod experiences a tensile stress of $10^8\text{ N/m}^2$. If the Young's modulus of the metal is $2 \times 10^{11}\text{ N/m}^2$, what is the strain energy stored per unit volume of the rod?

A heavy metallic wire of length 10 m, density $\rho = 8000\text{ kg/m}^3$, and Young's modulus $Y = 2 \times 10^{11}\text{ N/m}^2$ hangs vertically from a rigid ceiling. Taking $g = 10m/s^2$, what is the elongation of the wire due to its own weight?

A metal rod of Young's modulus $1.2 \times 10^{11}\text{ N/m}^2$ and coefficient of linear expansion $\alpha = 10^{-5}\text{ /}^\circ\text{C}$ is clamped tightly between two rigid supports. If the temperature increases by $50^\circ\text{C}$, what is the thermal stress developed in the rod?

A solid sphere is subjected to a uniform hydraulic pressure of $2 \times 10^6\text{ N/m}^2$. If the fractional change in its volume is 0.1%, what is the Bulk modulus of the material of the sphere?

Two wires A and B are made of the same material. Wire A has length $L$ and radius $r$, while wire B has length $2L$ and radius $2r$. If both wires are subjected to the same stretching force, what is the ratio of elongation of wire A to wire B ($\Delta L_A : \Delta L_B$)?

Based on the setup described, what is the shearing strain experienced by the cube?

A constant stretching force of 50 N elongates a metal wire by 2 mm. How much elastic work is performed in stretching the wire?

What are the practical (experimental) lower and upper limits of Poisson's ratio ($\sigma$) for common real physical materials?

A cylindrical wire with Poisson's ratio $\sigma = 0.25$ experiences a longitudinal strain of $4 \times 10^{-3}$. What is the magnitude of the lateral strain in the wire?

A metal wire supports a maximum load $F$ before breaking. If a second wire of the exact same material has twice the diameter, what maximum breaking load can it support?

Two wires of identical material and length have radii in the ratio $1 : 2$. If both are stretched by equal forces $F$, what is the ratio of elastic potential energy stored in the first wire to the second wire ($U_1 : U_2$)?

For an isotropic solid material, the relation connecting Young's modulus ($Y$), Shear modulus ($\eta$), and Poisson's ratio ($\sigma$) is given by $Y = 2\eta(1 + \sigma)$. If $\sigma = 0.25$, what is the ratio $Y / \eta$?

Based on the table above, which material sample exhibits the highest resistance to longitudinal deformation (highest stiffness)?

If the Bulk modulus of a liquid is $4.0 \times 10^9\text{ N/m}^2$, what is the compressibility of the liquid?

In a standard stress-strain curve for a ductile metal, what is the point beyond which the material undergoes permanent plastic deformation?

A flexible rubber cord of length $L$ is stretched until its new length becomes $2L$. What is the tensile strain produced in the cord?

What is the ratio of tensile stress developed in Rod 1 to that in Rod 2?

What physical quantity is represented by the area inside an elastic hysteresis loop on a stress-strain graph for a rubber sample?

A metal cylinder undergoes uniform axial compression. If the fractional decrease in its radius is 1% and the fractional decrease in its length is 2%, what is the overall fractional decrease in its volume?