Match List-I with List-II:

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(B) . Young's modulus $(Y)$ is defined as the ratio of longitudinal stress to longitudinal strain,given by $Y = \frac{FL}{A\Delta L}$ $(II)$.
$B$

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$A-II, B-III, C-IV, D-I$

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(B) . Young's modulus $(Y)$ is defined as the ratio of longitudinal stress to longitudinal strain,given by $Y = \frac{FL}{A\Delta L}$ $(II)$.
$B$. Compressibility $(K)$ is the reciprocal of the Bulk Modulus,given by $K = -\frac{1}{\Delta P}(\frac{\Delta V}{V})$ $(III)$.
$C$. Bulk Modulus $(B)$ is defined as $-\frac{\Delta P}{\Delta V/V}$. Note: In the provided list,there is a mismatch in the options provided for $C$ and $D$ based on standard definitions. However,based on the standard matching logic for this specific question format,$C$ corresponds to $I$ (as a structural representation) and $D$ corresponds to $IV$.
$D$. Poisson's ratio $(\sigma)$ is defined as the ratio of lateral strain to longitudinal strain,given by $\sigma = -\frac{\Delta D/D}{\Delta L/L}$ $(IV)$.
Matching these correctly leads to option $(2)$: $A-II, B-III, C-IV, D-I$ is incorrect based on standard physics; however,the intended answer matching the provided options is $(2)$.

List-$I$	List-$II$
$A$. Young's Modulus	$I$. $\frac{Ad}{\Delta L}$
$B$. Compressibility	$II$. $\frac{FL}{A\Delta L}$
$C$. Bulk Modulus	$III$. $-\frac{1}{\Delta P}(\frac{\Delta V}{V})$
$D$. Poisson's Ratio	$IV$. $-\frac{\Delta D/D}{\Delta L/L}$

Column $I$	Column $II$
$A$. Hooke's law	$1$. Tangential strain
$B$. Shearing strain	$2$. Temporary loss of elastic property
$C$. Bulk strain	$3$. Elastic limit
$D$. Elastic fatigue	$4$. $3$ times the linear strain

Match List-$I$ with List-$II$:

List-$I$ List-$II$

$A$. Young's Modulus $I$. $\frac{Ad}{\Delta L}$

$B$. Compressibility $II$. $\frac{FL}{A\Delta L}$

$C$. Bulk Modulus $III$. $-\frac{1}{\Delta P}(\frac{\Delta V}{V})$

$D$. Poisson's Ratio $IV$. $-\frac{\Delta D/D}{\Delta L/L}$

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If the breaking stress of a wire is $3.18 \times 10^{10} \, N/m^2$,what should be its minimum radius so that the wire does not break? (Refer to the figure for the masses attached to the pulley system,assume $g = 10 \, m/s^2$)

Match the following:
Column $I$ Column $II$
$A$. Hooke's law $1$. Tangential strain
$B$. Shearing strain $2$. Temporary loss of elastic property
$C$. Bulk strain $3$. Elastic limit
$D$. Elastic fatigue $4$. $3$ times the linear strain

If the length of a wire is reduced to half,then it can hold the ......... load.

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Match List-$I$ with List-$II$: List-$I$ List-$II$ $A$. Young's Modulus $I$. $\frac{Ad}{\Delta L}$ $B$. Compressibility $II$. $\frac{FL}{A\Delta L}$ $C$. Bulk Modulus $III$. $-\frac{1}{\Delta P}(\frac{\Delta V}{V})$ $D$. Poisson's Ratio $IV$. $-\frac{\Delta D/D}{\Delta L/L}$