Two blocks of masses $1 \,kg$ and $2 \,kg$ are connected by a metal wire going over a smooth pulley. The breaking stress of metal is $\frac{40}{3 \pi} \times 10^6 \,N m^{-2}$. What should be the minimum radius of the wire used if it should not break (in $mm$)? $(g = 10 \,m s^{-2})$

$A$ 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)

Which of the following materials is non-crystalline?

$A$ metal wire is clamped between two vertical walls. At $20 ^o C$,the unstrained length of the wire is exactly equal to the separation between the walls. If the temperature of the wire is decreased,the graph between elastic energy density $(u)$ and temperature $(T)$ of the wire is:

$A$ solid that transmits light in the visible region and has a very low melting point possesses:

The two thigh bones (femurs),each of cross-sectional area $10 \; cm^{2}$,support the upper part of a human body of mass $40 \; kg$. Estimate the average pressure sustained by the femurs.