If the breaking force for a given wire is $F$, then the breaking force of two wires of the same material and same dimensions joined together in parallel will be

$A$ uniform wire of length $l$ and weight $w$ is suspended from the roof with a weight $W$ attached at the other end. The stress in the wire at a distance $l/3$ from the top is given by $(\frac{W}{A} + \gamma \frac{w}{A})$, where $A$ is the cross-sectional area of the wire. The value of $\gamma$ is . . . . . . .

Potassium has a $bcc$ structure with a nearest neighbour distance of $4.525 \ \mathring{A}$. Its atomic weight is $39$. Its density in $kg/m^{3}$ is:

Two blocks of masses $1 \, kg$ and $2 \, kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 \, N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 \, m/s^2$.

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

One end of a wire of $8 \,mm$ radius and $100 \,cm$ length is fixed and the other end is twisted through an angle of $45^{\circ}$. The angle of shear is (in $^{\circ}$)