Class 11PhysicsMechanical Properties of SolidsBasic of Elasticity, Stress and Strain relationship and Graphical analysis
EasyWhat is stress? Write its unit and dimensional formula.
(N/A) Stress is defined as the restoring force per unit area of a body that has been deformed by an external force. Mathematically,$\text{Stress} = \frac{F}{A}$,where $F$ is the restoring force and $A$ is the cross-sectional area.
The $SI$ unit of stress is $\text{Pascal (Pa)}$ or $\text{N/m}^2$.
The dimensional formula of stress is calculated as: $\text{Dimension of Force} = [MLT^{-2}]$ and $\text{Dimension of Area} = [L^2]$.
Therefore,$\text{Dimension of Stress} = \frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]$.
The $SI$ unit of stress is $\text{Pascal (Pa)}$ or $\text{N/m}^2$.
The dimensional formula of stress is calculated as: $\text{Dimension of Force} = [MLT^{-2}]$ and $\text{Dimension of Area} = [L^2]$.
Therefore,$\text{Dimension of Stress} = \frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]$.
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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:
The elastic limit for a gas
Easy
View SolutionMatch the physical quantities in Column-$I$ with the details given in Column-$II$ appropriately:
Column-$I$ Column-$II$ $(a)$ $\text{Stress} \propto \text{Strain}$ $(i)$ $M^1 L^{-1} T^{-2}$ $(b)$ $\text{Dimensional formula for compressibility}$ $(ii)$ $M^{-1} L^1 T^2$ $(iii)$ $\text{Poisson's ratio}$ $(iv)$ $\text{Hooke's law}$
| Column-$I$ | Column-$II$ |
|---|---|
| $(a)$ $\text{Stress} \propto \text{Strain}$ | $(i)$ $M^1 L^{-1} T^{-2}$ |
| $(b)$ $\text{Dimensional formula for compressibility}$ | $(ii)$ $M^{-1} L^1 T^2$ |
| $(iii)$ $\text{Poisson's ratio}$ | |
| $(iv)$ $\text{Hooke's law}$ |
Easy
View Solution$A$ rod of constant cross-section moves towards the right with constant acceleration $a$. The graph of stress versus distance from the left end is shown in the figure. If the density of the material of the rod at cross-section $1$ is $9 \text{ g/cm}^3$,find the density at cross-section $2$ in $\text{g/cm}^3$.
Which one of the following is the weakest kind of bonding in solids?
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