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 $= 12.5 \times 10^{11} \,dyne/cm^2$)

What force is required to increase the length of a wire of diameter $4 \, mm$ and Young's modulus $9 \times 10^{10} \, N/m^2$ by $0.1\%$?

The area of cross-section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} \, m^2$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to $25$ metric tons,the required area of cross-section of the rope should be $......... \times 10^{-4} \, m^2$ (take $g = 10 \, m/s^2$).

$A$ uniformly tapering conical wire is made from a material of Young's modulus $Y$ and has a normal,unextended length $L$. The radii at the upper and lower ends of this conical wire have values $R$ and $3R$,respectively. The upper end of the wire is fixed to a rigid support and a mass $M$ is suspended from its lower end. The equilibrium extended length of this wire would be:

The area of cross-section of a wire of length $1.1 \, m$ is $1 \, mm^2$. It is loaded with $1 \, kg$. If Young's modulus of copper is $1.1 \times 10^{11} \, N/m^2$,then the increase in length will be ......... $mm$ (Take $g = 10 \, m/s^2$)

There is some change in length when a $33000 \,N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \,m^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 \times 10^{11} \,N/m^2$ and the coefficient of linear expansion of steel is $1.1 \times 10^{-5} /{ }^{\circ}C$). (in $^{\circ}C$)