Stress and Strain

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free end. The longitudinal stress at any point of cross-sectional area $A$of the wire is:

A metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter $14 \mathrm{mm}$. The tensile stress developed in the wire under equilibrium state is $7\times {10}^5 \mathrm{N} {\mathrm{m}}^{–2}$. The value of mass $m$ is ______ $\mathrm{kg}$.

(Take $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$ and $\pi =\frac{22}{7}$)

A hydraulic automobile lift is designed to lift vehicles of mass $5000 \mathrm{kg}$. The area of cross section of the cylinder carrying load is $250 {\mathrm{cm}}^2$. The maximum pressure the smaller piston would have to bear is [Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$]

The density of a metal at normal pressure is $\rho$. Its density when it is subjected to an excess pressure$p$ is $\rho \text{'}$. If $B$ is Bulk modulus of the metal, the ratio of $\frac{\rho \text{'}}{\rho }$ is: 
 

What is the greatest length of copper wire that can hang without breaking? Breaking stress $= 7.2\times {10}^7 \mathrm{N}/{\mathrm{m}}^2$, Density of copper $= 7.2 \mathrm{g}/\mathrm{cc}$, $g= 10 \mathrm{m}/{\mathrm{s}}^2$.

When normal stress acts on a body it changes the 

The linear strain in $x,y$ and $z$ directions are $e_x$, $e_y$ and $e_z$ respectively. Then the volumetric strain is given by

What is an elastomer ?

How should we apply a force on a body to produce shearing stress ?

What is the difference between tensile stress and volume stress?

Define stress. Give its dimensional formula.

Define strain. Name the three types of strain.

A solid object having uniform density $\left(\rho \right)$ and varying cross-sectional area (which is circular) is placed on smooth horizontal surface as shown. Then the value of $\frac{R_1}{R_2}$ if the stress throughout its height remains same and having value equal to $\mathrm{c}$.

A stone of $0.5\mathrm{kg}$ mass is attached to one end of a $0.8\mathrm{m}$ long aluminum wire of $0.7\mathrm{mm}$ diameter and suspended vertically. The stone is now rotated in a horizontal plane at a rate such that wire makes an angle of ${85}^0$ with the vertical. If $Y=7\times {10}^{10}{\mathrm{Nm}}^{-2}$, $\sin 85°=0.9962$ and $\cos 85°=0.0872$, the increase in length of wire is

The Poisson's ratio of the material of a wire whose volume remains constant under an external normal stress is _____

Explain compressive stress with an example.

What is the dimensional formula for strain?

Write down the unit of strain.

What are strain and its properties?

What are the dimensions of stress?