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	$IV$. $-\frac{\Delta D/D}{\Delta L/L}$

$A$ string $AB$ of unstretched length $L$ is stretched by applying a force $F$ at the mid-point $C$ such that the segments $AC$ and $BC$ make an angle $\theta$ with $AB$ as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio $K$. The force $F$ is given by

In order to determine the Young's Modulus of a wire of radius $0.2 \, cm$ (measured using a scale of least count $= 0.001 \, cm$) and length $1 \, m$ (measured using a scale of least count $= 1 \, mm$),a weight of mass $1 \, kg$ (measured using a scale of least count $= 1 \, g$) was hanged to get the elongation of $0.5 \, cm$ (measured using a scale of least count $= 0.001 \, cm$). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in $\%$)

$A$ solid that transmits light in the visible region and has a very low melting point possesses:

Match the following:

Column-$I$	Column-$II$
$(A)$ Shear modulus	$(I)$ Resistance to change in volume
$(B)$ Shearing stress	$(II)$ Proportionality constant
$(C)$ Elastic fatigue	$(III)$ Tangential stress
$(D)$ Modulus of elasticity	$(IV)$ Temporary loss of elastic property
	$(V)$ Resistance to change against deformation force

The correct match is:

Read the following two statements below carefully and state,with reasons,if it is true or false.
$(a)$ The Young's modulus of rubber is greater than that of steel;
$(b)$ The stretching of a coil is determined by its shear modulus.