Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $1:\sqrt 2 $. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

Force constant of a spring $(K)$ is synonymous to

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 and other end is subjected to elongation. The stress requires to produced a new elongation of $0.2\,mm$ is [Given, the Young’s Modulus for steel and brass are respectively $120\times 10^9\,N/m^2$ and $60\times 10^9\,N/m^2$ ]

A $14.5\; kg$ mass, fastened to the end of a steel wire of unstretched length $1.0 \;m ,$ is whirled in a vertical circle with an angular velocity of $2\;rev/s$ at the bottom of the circle. The cross-sectional area of the wire is $0.065 \;cm ^{2} .$ Calculate the elongation of the wire when the mass is at the lowest point of its path.

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ}$ with the load axis. The length of wire is $62.8\,cm$ and its diameter is $4\,mm$. The Young's modulus is found to be $x \times$ $10^4\,Nm ^{-2}$. The value of $x$ is

A uniform wire (Young's modulus $2 \times 10^{11}\, Nm^{-2}$ ) is subjected to longitudinal tensile stress of $5 \times 10^7\,Nm^{-2}$ . If the over all volume change in the wire is $0.02\%,$ the fractional decrease in the radius of the wire is close to