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:

The ratio of the lengths of two wires of the same material is $1:2$ and the ratio of their radii is $1:\sqrt{2}$. If they are stretched by the same force,what is the ratio of the increase in their lengths?

An object of mass $15 \,kg$ is attached to the end of a metal wire of unstretched length $1.0 \,m$. The object is then whirled in a vertical circle with an angular velocity of $4 \,rad/s$ at the bottom of the circle. If the cross-sectional area of the wire is $0.05 \,cm^2$ and Young's modulus of the metal is $2 \times 10^{11} \,N/m^2$, then calculate the elongation of the wire when the mass is at the lowest point of its path. (Take $g = 10 \,m/s^2$) (in $\,mm$)

Two wires $A$ and $B$ of the same material have radii in the ratio $2:1$ and lengths in the ratio $4:1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is .......

Two wires $A$ and $B$ are made of the same material. Their diameters are in the ratio of $1: 2$ and their lengths are in the ratio of $1: 3$. If they are stretched by the same force,then the increase in their lengths will be in the ratio of:

The ratio of Young's modulus of three wires is $2 : 2 : 1$ and the ratio of their cross-sectional areas is $1 : 2 : 3$. If the same force is applied to each,what is the ratio of the increase in their lengths?