If the breaking force for a given wire is $F$, then the breaking force of two wires of the same material and same dimensions joined together in parallel will be

$A$ 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:

$A$ 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 $1.5 \,mm$?

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

$A$ 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

Due to the addition of impurities,the modulus of elasticity