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:

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.

To break a wire,a breaking stress of $10^6 \, N/m^2$ is required. If the density of the material is $3 \times 10^3 \, kg/m^3$,then the length of the wire which will break by its own weight will be......... $m$ (Take $g = 10 \, m/s^2$)

$A$ rod of length $1.05 \; m$ having negligible mass is supported at its ends by two wires of steel (wire $A$) and aluminium (wire $B$) of equal lengths as shown in Figure. The cross-sectional areas of wires $A$ and $B$ are $1.0 \; mm^{2}$ and $2.0 \; mm^{2}$ respectively. At what point along the rod should a mass $m$ be suspended in order to produce $(a)$ equal stresses and $(b)$ equal strains in both steel and aluminium wires?

$A$ wire of length $5 \,m$ is twisted through $30^{\circ}$ at its free end. If the radius of the wire is $1 \,mm$,the shearing strain in the wire is: (in $^{\circ}$)

What are the factors on which the modulus of elasticity depends?