$A$ bob of mass $10\, kg$ is attached to a wire $0.3\, m$ long. Its breaking stress is $4.8 \times 10^7\, N/m^2$. The area of cross-section of the wire is $10^{-6}\, m^2$. The maximum angular velocity with which it can be rotated in a horizontal circle is ....... $rad/sec$.

Two identical wires of rubber and iron are stretched by the same weight. The number of atoms in the iron wire will be:

$A$ sphere of mass $4 \,kg$ is attached to one end of a steel wire of length $1 \,m$ and radius $1 \,mm$. It is whirled in a vertical circle with an angular velocity $10 \,rad \,s^{-1}$. If the sphere is at the lowest point of its path,the elongation in the wire is . . . . . . $(g=10 \,ms^{-2}, Y_{\text{steel}}=20 \times 10^{10} \,Nm^{-2})$ (in $\,mm$)

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:

$A$ metal rod of cross-sectional area $10^{-4} \, m^{2}$ is hanging in a chamber kept at $20^{\circ} C$ with a weight attached to its free end. The coefficient of thermal expansion of the rod is $2.5 \times 10^{-6} \, K^{-1}$ and its Young's modulus is $4 \times 10^{12} \, N/m^{2}$. When the temperature of the chamber is lowered to $T$,a weight of $5000 \, N$ needs to be attached to the rod so that its length remains unchanged. Then,$T$ is ............ $^{\circ} C$.

$A$ steel wire is suspended vertically from a rigid support. When loaded with a weight in air,it extends by $l_a$ and when the weight is immersed completely in water,the extension is reduced to $l_w$. Then the relative density of the material of the weight is