A copper wire of length 1.0, m and a steel wire of length 0.5, m having equal cross-sectional areas

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8.Mechanical Properties of Solids

medium

A copper wire of length $1.0\, m$ and a steel wire of length $0.5\, m$ having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by $1\, mm$. If the Young's modulii of copper and steel are respectively $1.0\times10^{11}\, Nm^{-2}$ and $2.0\times10^{11}\, Nm^{- 2}$, the total extension of the composite wire is ........ $mm$

$1.75$

$2$

$1.50$

$1.25$

(JEE MAIN-2013)

Solution

${Y_c} \times \left( {\Delta {L_c}/{L_c}} \right) = {Y_s} \times \left( {\Delta {L_s}/{L_s}} \right)$

$ \Rightarrow 1 \times {10^{11}} \times \left( {\frac{{1 \times {{10}^{ – 3}}}}{1}} \right) = 2 \times {10^{11}} \times \left( {\frac{{\Delta {L_s}}}{{0.5}}} \right)$

$\therefore \Delta {L_s} = \frac{{0.5 \times {{10}^{ – 3}}}}{2} = 0.25\,mm$

Therefore, total extension of the composite

$wire = \Delta {L_c} + \Delta {L_s}$

$ = 1\,mm + 0.25\,m = 1.25\,m$

Standard 11

Physics

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Column$-II$ is related to Column$-I$. Join them appropriately :

Column $-I$ Column $-II$

$(a)$ When temperature raised Young’s modulus of body $(i)$ Zero

$(b)$ Young’s modulus for air $(ii)$ Infinite

$(iii)$ Decreases

$(iv)$Increases

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medium

Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$. How far does the midpoint $A$ move ………… $mm$

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medium

Column $-I$	Column $-II$
$(a)$ When temperature raised Young’s modulus of body	$(i)$ Zero
$(b)$ Young’s modulus for air	$(ii)$ Infinite
	$(iii)$ Decreases
	$(iv)$Increases

Solution

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Column$-II$ is related to Column$-I$. Join them appropriately :

Column $-I$ Column $-II$

$(a)$ When temperature raised Young’s modulus of body $(i)$ Zero

$(b)$ Young’s modulus for air $(ii)$ Infinite

$(iii)$ Decreases

$(iv)$Increases