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?

What is the effect of change in temperature on the Young's modulus?

What is the percentage increase in length of a wire of diameter $2.5 \,mm$,stretched by a force of $100 \,kg$ wt? (Young's modulus of elasticity of wire $= 12.5 \times 10^{11} \,dyne/cm^2$)

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

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 .......

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 $\,mm$)