Each of three blocks $P$,$Q$ and $R$ shown in the figure has a mass of $3 \,kg$. Each of the wires $A$ and $B$ has a cross-sectional area of $0.005 \,cm^2$ and a Young's modulus of $2 \times 10^{11} \,N \,m^{-2}$. Neglecting friction,the longitudinal strain on wire $B$ is . . . . . . $\times 10^{-4}$. (Take $g=10 \,m/s^2$)

What is the tangential stress on the cross-section $PQRS$?

$A$ 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 ............ $^{\circ} C$.

When a shearing force is applied to a body,elastic potential energy is stored in it. Upon removing the force,this energy:

$A$ 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 ....... $rad/sec$.

The density and breaking stress of a wire are $6 \times 10^4 \ kg/m^3$ and $1.2 \times 10^8 \ N/m^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}$ of the value on the surface of Earth. The maximum length of the wire without breaking is ............ $m$ (take $g = 10 \ m/s^2$ on Earth).