If the length of a wire is made double and the radius is halved of its respective values,then the Young's modulus of the material of the wire will:

$A$ thick metal wire of density $\rho$ and length $L$ is hung from a rigid support. The increase in length of the wire due to its own weight is ($Y =$ Young's modulus of the material of the wire).

$A$ steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^{\circ}C$ so that it cannot contract on cooling. The tension in the rod at $0\,^{\circ}C$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^{\circ}C, Y = 2 \times 10^{11}\,N/m^2)$

Which of the following graphs correctly depicts the spring constant $k$ versus the length $l$ of the spring?

$A$ $3 \ m$ 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 $g = 3 \pi \ m/s^2$)

$A$ uniform steel rod of mass $1.8 \,kg$ and length $0.8 \,m$ is hung from a nail with the help of two steel wires,each of area of cross-section $0.01 \,mm^2$ and unstretched length $0.5 \,m$,as shown in the figure. The centre of mass of the rod lies vertically below the nail. The increase in the distance between the centre of mass of the rod and the nail due to stretching of the wires as the rod hangs is . . . . . . $mm$. (Young's modulus of steel $= 2 \times 10^{11} \,N/m^2$ and acceleration due to gravity $= 10 \,m/s^2$)