$A$ steel rod with $Y = 2.0 \times 10^{11} \, N/m^2$ and $\alpha = 10^{-5} \, ^\circ C^{-1}$ of length $4 \, m$ and area of cross-section $10 \, cm^2$ is heated from $0^\circ C$ to $400^\circ C$ without being allowed to extend. The tension produced in the rod is $x \times 10^5 \, N$ where the value of $x$ is ....... .

In an experiment,brass and steel wires of length $1\,m$ each with areas of cross-section $1\,mm^2$ are used. The wires are connected in series and one end of the combined wire is connected to a rigid support,while the other end is subjected to an elongation. The stress required to produce a total elongation of $0.2\,mm$ is: [Given: Young's Modulus for steel and brass are $120 \times 10^9\,N/m^2$ and $60 \times 10^9\,N/m^2$ respectively]

$A$ steel wire of $1 \, m$ long and $1 \, mm^2$ cross-sectional area is hung from a rigid support. When a weight of $1 \, kg$ is hung from it,the change in length will be given by ..... $mm$ $(Y = 2 \times 10^{11} \, N/m^2, g = 10 \, m/s^2)$.

As shown in the figure,a light uniform rod $PQ$ of length $150 \ cm$ is suspended from the ceiling horizontally using two metal wires $A$ and $B$ tied to the ends of the rod. The ratios of the radii and the Young's moduli of the materials of the two wires $A$ and $B$ are respectively $2:3$ and $3:2$. The position at which a weight should be suspended from the rod such that the elongations of the two wires become equal is

$A$ rod of uniform cross-sectional area $A$ and length $L$ has a weight $W$. It is suspended vertically from a fixed support. If Young's modulus for the rod is $Y$,then the elongation produced in the rod due to its own weight is:

$A$ $500 \,g$ ball is attached to one end of an aluminum wire of area of cross-section $0.5 \,mm^2$ and an unstretched length of $1.4 \,m$. The other end of the wire is fixed to the top of a vertical pole. The ball rotates about the pole in a horizontal plane such that the angle between the wire and the horizontal is $30^{\circ}$. The increase in the length of the wire is . . . . . . $mm$. (Young's modulus of aluminum $= 0.7 \times 10^{11} \,N/m^2$ and acceleration due to gravity $= 10 \,m/s^2$)