If the temperature of a wire of length $2 \,m$ and area of cross-section $1 \,cm ^2$ is increased from $0^{\circ} C$ to $80^{\circ} C$ and is not allowed to increase in length, then force required for it is ............$N$ $\left\{Y=10^{10} \,N / m ^2, \alpha=10^{\left.-6 /{ }^{\circ} C \right\}}\right.$

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?

The Young's modulus of a steel wire of length $6\,m$ and cross-sectional area $3\,mm ^2$, is $2 \times 11^{11}\,N / m ^2$. The wire is suspended from its support on a given planet. A block of mass $4\,kg$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the earth. The elongation of wire is  (Take $g$ on the earth $=10$ $\left.m / s ^2\right):$

A structural steel rod has a radius of $10 \;mm$ and a length of $1.0 \;m$. A $100 \;kN$ force stretches it along its length. Calculate $(a)$ stress, $(b)$ elongation, and $(c)$ strain on the rod. Young's modulus, of structural steel $1 s 2.0 \times 10^{11} \;N m ^{-2}$

With rise in temperature, the Young's modulus of elasticity

Steel and copper wires of same length are stretched by the same weight one after the other. Young's modulus of steel and copper are $2 \times {10^{11}}\,N/{m^2}$ and $1.2 \times {10^{11}}\,N/{m^2}$. The ratio of increase in length