When a weight of $10 \,kg$ is suspended from a copper wire of length $3 \,m$ and diameter $0.4 \,mm$, its length increases by $2.4 \,cm$. If the diameter of the wire is doubled, then the extension in its length will be (in $\,cm$)

$A$ $3 \ m$ long wire of radius $3 \ mm$ shows an extension of $0.1 \ mm$ when loaded vertically by a mass of $50 \ kg$ in an experiment to determine Young's modulus. The value of Young's modulus of the wire as per this experiment is $P \times 10^{11} \ Nm^{-2}$,where the value of $P$ is: (Take $g = 3 \pi \ m/s^2$)

If the given graph shows the load $(W)$ attached to and the elongation $(\Delta l)$ produced in a wire of length $1 \,m$ and area of cross-section $1 \,mm^2$, then the Young's modulus of the material of the wire is

Two wires of different materials have same length $L$ and same diameter $d$. The second wire is connected at the end of the first wire and forms one single wire of double the length. This wire is subjected to a stretching force $F$ to produce an elongation $\ell$. The two wires have:

The pressure to be applied to the ends of a steel cylinder to keep its length constant upon raising its temperature by $100^{\circ} C$ is (thermal expansion coefficient,$\alpha = 11 \times 10^{-6} / K$,Young's modulus $Y = 200 \text{ GPa}$)

The length of a metal wire is found to be $L_1$ and $L_2$ when the tensions $T_1$ and $T_2$ are applied to it respectively. The natural length of the wire is