Stress versus strain graphs for wires of two materials A and B are as shown in figure. If {Y

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8.Mechanical Properties of Solids

medium

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If ${Y_A}$ and ${Y_B}$ are the Young ‘s modulii of the materials, then

${Y_B} = 2{Y_A}$

${Y_A} = {Y_B}$

${Y_B} = 3{Y_A}$

${Y_A} = 3{Y_B}$

Solution

(d) $\frac{{{Y_A}}}{{{Y_B}}} = \frac{{\tan {\theta _A}}}{{\tan {\theta _B}}} = \frac{{\tan 60}}{{\tan 30}} = \frac{{\sqrt 3 }}{{1/\sqrt 3 }} = 3 \Rightarrow {Y_A} = 3{Y_B}$

Standard 11

Physics

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1m$ suspended from the top of a roof at one end with a load $W$ connected to the other end. If the cross sectional area of the wire is ${10^{ – 6}}{m^2},$ calculate the young’s modulus of the material of the wire

medium

(IIT-2003)

A uniform dense rod with non uniform young's modulus is hanging from ceiling under gravity. If elastic energy density at every point is same then young's modulus with $x$ will change as which of the shown graph

normal

In Column$-I$ there are two graphs and in Column$-II$ whose graph is for this are given. Join them appropriately :

Column $-I$ Column $-II$

$(a)$ image $(i)$ $A$ is ductile

$(b)$ image $(ii)$ $A$ is brittle

$(iii)$ $B$ is ductile

$(iv)$ $B$ is brittle

medium

The graph is drawn between the applied force $F$ and the strain $(x)$ for a thin uniform wire. The wire behaves as a liquid in the part

easy

The load versus strain graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line

medium

Column $-I$	Column $-II$
$(a)$ image	$(i)$ $A$ is ductile
$(b)$ image	$(ii)$ $A$ is brittle
	$(iii)$ $B$ is ductile
	$(iv)$ $B$ is brittle

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If ${Y_A}$ and ${Y_B}$ are the Young ‘s modulii of the materials, then

Solution

Similar Questions

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1m$ suspended from the top of a roof at one end with a load $W$ connected to the other end. If the cross sectional area of the wire is ${10^{ – 6}}{m^2},$ calculate the young’s modulus of the material of the wire

A uniform dense rod with non uniform young's modulus is hanging from ceiling under gravity. If elastic energy density at every point is same then young's modulus with $x$ will change as which of the shown graph

In Column$-I$ there are two graphs and in Column$-II$ whose graph is for this are given. Join them appropriately : Column $-I$ Column $-II$ $(a)$ image $(i)$ $A$ is ductile $(b)$ image $(ii)$ $A$ is brittle $(iii)$ $B$ is ductile $(iv)$ $B$ is brittle

The graph is drawn between the applied force $F$ and the strain $(x)$ for a thin uniform wire. The wire behaves as a liquid in the part

The load versus strain graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line

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In Column$-I$ there are two graphs and in Column$-II$ whose graph is for this are given. Join them appropriately :

Column $-I$ Column $-II$

$(a)$ image $(i)$ $A$ is ductile

$(b)$ image $(ii)$ $A$ is brittle

$(iii)$ $B$ is ductile

$(iv)$ $B$ is brittle