Mechanical properties of solids practice · Medium

An elastic material of Young’s modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is

What is the Young's modulus of elasticity for a perfectly rigid body?

The pressure of a medium is changed from $1.01 \times {10^5}$ Pa to $1.165\,\, \times {10^5}$ Pa and change in volume is $10\,\,\%$ keeping temperature constant. The Bulk modulus of the medium is

Statement I: A hollow shaft is found to be stronger than a solid shaft made of same material.
Statement II: The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.

A: Diamond is more elastic than rubber.
R: When same deforming force is applied diamond deforms less than rubber.

A mass of $100 \mathrm{~gram}$ is attached to the end of a rubber string $49 \mathrm{~cm}$ long and having an area of cross-section $20 \mathrm{~mm}^2$. The string is whirled round, horizontally at a constant speed of $40 \mathrm{~rps}$ in a circle of radius $51 \mathrm{~cm}$. Find Young's modulus of rubber.

A wire of length L and cross-section A is made of material of Young’s modulus Y. It is stretched by an amount x, the work done is

A metal rod of Young’s modulus $2 \times {10^{10}}\,N{m^{ - 2}}$ undergoes an elastic strain of $0.2\%$. The energy per unit volume stored in the rod in $joule/{m^3}$ is

Cross sectional area of a wire $\left(\mathrm{Y}=5 \times 10^{11}\right.$ $\mathrm{N} / \mathrm{m}^2$ ) is $0.1 \mathrm{~cm}^2$. Find the force required to make its length double.

A $14.5 \mathrm{~kg}$ mass, fastened to the end of a steel wire of unstretched length $1 \mathrm{~m}$, is whirled in a vertical circle with an angular velocity of $2 \mathrm{~rev} / \mathrm{s}$ at the bottom of the circle. The cross-sectional area of the wire is $0.065 \mathrm{~cm}^2$. The elongation of the wire when the mass is at the lowest point of its path is;

$\text {[ } Y_{\text {steel }}=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2 \text { ] }$

A wire increases by $10^{-3}$ of its length when a stress of $1 \times 10^8 \mathrm{~Nm}^{-2}$ is applied to it. What is the Young's modulus of the material of the wire?