In a wire of length $L,$ the increase in its length is $l.$ If the length is reduced to half,the increase in its length will be

When the temperature of a wire of length $L_0$ is increased by $T$,what is the energy density? The volume expansion coefficient of the wire is $\gamma$ and the Young's modulus is $Y$.

$A$ metal bar of length $L$ and area of cross-section $A$ is clamped between two rigid supports. For the material of the rod,its Young's modulus is $Y$ and coefficient of linear expansion is $\alpha$. If the temperature of the rod is increased by $\Delta t ^\circ C$,the force exerted by the rod on the supports is

$A$ rubber cord $10\, m$ long is suspended vertically. How much does it stretch under its own weight? (Density of rubber is $1500\, kg/m^3$,$Y = 5 \times 10^8\, N/m^2$,$g = 10\, m/s^2$)

Write the equation of bending in a rod. Write the unit of bending and its dimensional formula.

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A$. If the length of the first wire is increased by $\Delta l$ on applying a force $F$,how much force is needed to stretch the second wire by the same amount?