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 ............$N$ $\left\{Y=10^{10} \,N / m ^2, \alpha=10^{\left.-6 /{ }^{\circ} C \right\}}\right.$

Two steel wires of same length but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force stretches the combination by $10\ mm$ . How far does the midpoint $A$ move ......... $mm$

If Young's modulus for a material is zero, then the state of material should be

The temperature of a wire of length $1$ metre and area of cross-section $1\,c{m^2}$ is increased from $0°C$ to $100°C$. If the rod is not allowed to increase in length, the force required will be $(\alpha = {10^{ - 5}}/^\circ C$ and $Y = {10^{11}}\,N/{m^2})$

The maximum elongation of a steel wire of $1 \mathrm{~m}$ length if the elastic limit of steel and its Young's modulus, respectively, are $8 \times 10^8 \mathrm{~N} \mathrm{~m}^{-2}$ and $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$, is:

Increase in length of a wire is $1\, mm$ when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius, the increase in length will be  ........ $mm$