The Young's modulus of a rubber string $8\, cm$ long and density $1.5\, kg/m^3$ is $5 \times 10^8\, N/m^2$. If it is suspended from the ceiling in a room,the increase in length due to its own weight will be:

$A$ rod of length $L$ at room temperature and uniform area of cross section $A$ is made of a metal having a coefficient of linear expansion $\alpha /^{\circ}C$. It is observed that an external compressive force $F$,applied on each of its ends,prevents any change in the length of the rod when its temperature rises by $\Delta T \, K$. The Young's modulus $Y$ for this metal is:

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

The length of a metal wire is $L_1$ when the tension is $T_1$ and $L_2$ when the tension is $T_2$. The unstretched length of the wire is:

Two wires of the same material have lengths in the ratio $1:2$ and diameters in the ratio $2:1$. If they are stretched by forces $F_A$ and $F_B$ respectively to produce the same extension,then the ratio $\frac{F_A}{F_B}$ is:

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 $Y$.