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:

$Dyne/cm^2$ is not a unit of

$A$ string of length $0.314 \text{ m}$ and Young's modulus $2 \times 10^{10} \text{ N/m}^2$ is connected to another string of length $B$ and Young's modulus both twice of those of $A$. This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass $0.8 \text{ kg}$. The net change in length of the combination is . . . . . . $\text{mm}$. (radius of both the strings is $0.2 \text{ mm}$ and acceleration due to gravity $= 10 \text{ m/s}^2$) (Mass of both strings is to be neglected as compared to the mass of load)

$A$ light rod of length $200\,cm$ is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and has a cross-section of $0.1\,cm^2$,and the other is made of brass with a cross-section of $0.2\,cm^2$. At what distance from the steel wire should a weight be hung along the rod to produce equal stresses in both wires?

Match the type of elasticity involved:

System	Type of Elasticity
$(i)$ Suspension fibre of galvanometer	$(a)$ Linear
$(ii)$ Bending of beam	$(b)$ Shear
$(iii)$ Cutting piece of paper	$(c)$ Bulk
$(iv)$ Mechanical waves in fluid	$(d)$ Shear

Two identical steel cubes (masses $50\,g$,side $1\,cm$) collide head-on face to face with a speed of $10\,cm/s$ each. Find the maximum compression of each. Young's modulus for steel $Y = 2 \times 10^{11}\,N/m^2$.