$A$ steel wire of diameter $2 \,mm$ has a breaking strength of $4 \times 10^5 \,N$. What is the breaking force in $\times 10^5 \,N$ for a similar steel wire of diameter $1.5 \,mm$?

$A$ body of mass $10 \ kg$ is attached to a wire of $0.3 \ m$ length. The 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

$A$ 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)

$A$ 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:

$A$ string $AB$ of unstretched length $L$ is stretched by applying a force $F$ at the mid-point $C$ such that the segments $AC$ and $BC$ make an angle $\theta$ with $AB$ as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio $K$. The force $F$ is given by

$A$ wire can be broken by applying a load of $200\, N$. The force required to break another wire of the same length and same material,but double in diameter,is .......... $N$.