$A$ wire extends by $1 \ mm$ when a force is applied. If double the force is applied to another wire of the same material and length but half the radius of the cross-section,what will be the elongation of the wire in $mm$?

Four uniform wires of the same material are stretched by the same force. The dimensions of the wires are given below. Which one has the minimum elongation?

An aluminum rod (Young's modulus $Y = 7 \times 10^9 \, N/m^2$) has a breaking strain of $0.2\%$. The minimum cross-sectional area of the rod required to support a load of $10^4 \, N$ is:

If the ratio of diameters,lengths and Young's moduli of steel and brass wires shown in the figure are $p, q$ and $r$ respectively,then the corresponding ratio of increase in their lengths would be

The ratio of Young's modulus of the material of two wires is $2 : 3.$ If the same stress is applied on both,then the ratio of elastic energy per unit volume will be

$A$ $14.5\; kg$ 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.